WASHINGTON — President Biden signaled a vast increase in America’s commitment to defeating Russia in Ukraine on Thursday as he asked Congress to authorize $33 billion for more artillery, antitank weapons and other hardware as well as economic and humanitarian aid.

The request represented an extraordinary escalation in American investment in the war, more than tripling the total emergency expenditures and putting the United States on track to spend as much this year helping the Ukrainians as it did on average each year fighting its own war in Afghanistan, or more.

“The cost of this fight is not cheap,” Mr. Biden said at the White House. “But caving to aggression is going to be more costly if we allow it to happen. We either back the Ukrainian people as they defend their country or we stand by as the Russians continue their atrocities and aggression in Ukraine.”

Mr. Biden also sent Congress a plan to increase the government’s power to seize luxury yachts, aircraft, bank accounts and other assets of Russian oligarchs tied to President Vladimir V. Putin and use the proceeds to help the Ukrainians. Just hours later, Congress passed legislation allowing Mr. Biden to use a World War II-era law to supply weapons to Ukraine on loan quickly.

The latest American pledge came as Moscow raised the prospect of a widening conflict with the West. Russian officials accused the United States and Poland of working together on a covert plan to establish control over western Ukraine and asserted that the West was encouraging Ukraine to launch strikes inside Russia, where gas depots and a missile factory have burned or been attacked in recent days.

A Russian missile strike setting off a fiery explosion in central Kyiv shattered weeks of calm in the capital and served as a vivid reminder that the violence in Ukraine has not shifted exclusively to the eastern and southern portions of the country, where Russia is now focusing its efforts to seize and control territory. Russian forces are making “slow and uneven” progress in that part of Ukraine but are struggling to overcome the same supply line problems that hampered their initial offensive, the Pentagon said.

The strike came on the same day that President Volodymyr Zelensky of Ukraine was meeting with António Guterres, the U.N. secretary general, just a few miles away in Kyiv, a visit that was no secret in Moscow. Mr. Guterres arrived in Ukraine, after sitting down with Mr. Putin in Moscow, in hopes of securing evacuation routes for besieged Ukrainian civilians and support for the prosecution of war crimes.

In the hours before the latest strike, Mr. Guterres toured the stunning wreckage in Borodianka, Bucha and Irpin, three suburbs of Kyiv that have borne the heavy cost of the fighting. Standing in front of a row of scorched buildings where dozens of people were killed, he called Russia’s invasion “an absurdity” and said, “There is no way a war can be acceptable in the 21st century.”

In his nightly address, Mr. Zelensky condemned the strike, saying it revealed Russia’s “true attitude to global institutions” and was an effort to “humiliate the U.N.” He vowed a “strong response” to that and other Russian attacks. “We still have to drive the occupiers out,” he said.

Just as the United States was ramping up its flow of arms to the battlefield, the German Parliament voted overwhelmingly to deliver heavy weapons to Ukraine, a largely symbolic move to show unity after the government announced the plan earlier this week.

A day after Russia cut off gas supplies to Poland and Bulgaria, the German chancellor, Olaf Scholz, said his country must be prepared for the possibility that Germany could be next. “We have to be ready for it,” Mr. Scholz told reporters in Tokyo, where he paid Prime Minister Fumio Kishida of Japan a visit to shore up ties between the two countries.

Russian strikes and Ukrainian counterattacks continued to batter eastern and southern battlegrounds in Ukraine, but Russian troops are advancing cautiously in this latest phase, able to sustain only several kilometers of progress each day, according to a Pentagon official speaking on the condition of anonymity to discuss operational details.

Despite having much shorter supply lines now than they did during the war’s first several weeks in Ukraine’s north, the Russians have not overcome their logistics problem, the Pentagon official said, citing slow shipments of food, fuel, weapons and ammunition.

Moscow now has 92 battalion groups fighting in eastern and southern Ukraine — up from 85 a week ago, but still well below the 125 it had in the first phase of the war, the official said. Each battalion group has about 700 to 1,000 troops.

Russia has amassed artillery to support its troops near the city of Izium, according to the latest assessment by the Institute for the Study of War, a research group. Russian forces have used the city as a strategic staging point for their assault in the east and probably seek to outflank Ukrainian defensive positions, the analysts said.

Since Wednesday, Russian troops have captured several villages west of the city, according to Ukraine’s Defense Ministry, with the likely aim of bypassing Ukrainian forces on two parallel roads running south, toward the cities of Barvinkove and Sloviansk.

A senior American diplomat accused Russia of engaging in systematic campaigns to topple local governments in occupied Ukraine and to detain and torture local officials, journalists and activists in so-called “filtration camps,” where some of them have reportedly disappeared.

The diplomat, Michael R. Carpenter, the American ambassador to the Organization for Security and Cooperation in Europe, said the United States has information that Russia is dissolving democratically elected local governments and has forced large numbers of civilians in occupied areas into camps for questioning.

The Ukrainian military said it was moving more troops to the border with Transnistria, a small breakaway region in Moldova, on Ukraine’s southwest flank, hundreds of miles from the fighting on the eastern front.

Ukraine ordered the reinforcements after it accused Russia this week of orchestrating a series of explosions in Transnistria, potentially as a pretext to attack Ukraine from the south and move on Odesa, Ukraine’s major Black Sea port. Russia has thousands of troops in Transnistria, which is controlled by Kremlin-backed separatists.

Russia sought to turn the tables by accusing Ukraine and its allies of being the ones to widen the war, citing the supposed secret Polish-American plan to control western Ukraine and the recent attacks on targets inside Russia. Maria Zakharova, the Russian Foreign Ministry’s spokeswoman, urged Kyiv and Western capitals to take seriously Russia’s statements “that further calls on Ukraine to strike Russian facilities would definitely lead to a tough response from Russia.”

Mykhailo Podolyak, an adviser to Mr. Zelensky, said Ukraine had a right to strike Russian military facilities and “will defend itself in any way.” Britain’s defense minister, Ben Wallace, also said Ukraine would be justified in using Western arms to attack military targets inside Russia, as he warned that the war could turn into a “slow-moving, frozen occupation, like a sort of cancerous growth in Ukraine.”

Speaking at the White House, Mr. Biden rejected Russian suggestions that the United States was waging a proxy war against Moscow. “It shows the desperation that Russia is feeling about their abject failure in being able to do what they set out to do in the first instance,” Mr. Biden said.

He likewise condemned Russian officials’ raising the specter of nuclear war. “No one should be making idle comments about the use of nuclear weapons or the possibility that they could use that,” Mr. Biden said. “It’s irresponsible.”

The massive aid package Mr. Biden unveiled on Thursday would eclipse all the spending by the United States so far on the war. There is widespread bipartisan support on Capitol Hill for more aid, but it remained uncertain whether the issue could get tied up in negotiations over ancillary issues like pandemic relief or immigration.

The request, more than twice the size of the $13.6 billion package lawmakers approved and Mr. Biden signed last month, was intended to last through the end of September, underscoring the expectations of a prolonged conflict.

It includes more than $20 billion for security and military assistance, including $11.4 billion to fund equipment and replenish stocks already provided to Ukraine, $2.6 billion to support the deployment of American troops and equipment to the region to safeguard NATO allies and $1.9 billion for cybersecurity and intelligence support.

The request also includes $8.5 billion in economic assistance for the government in Kyiv to provide basic economic support, including food and health care services, as the Ukrainian economy reels from the toll of the war. An additional $3 billion would be provided for humanitarian assistance and food security funding, including medical supplies and support for Ukrainian refugees and to help stem the impact of the disrupted food supply chain.

When combined with the previous emergency measure, the United States would be authorizing $46.6 billion for the Ukraine war, which represents more than two-thirds of Russia’s entire annual defense budget of $65.9 billion. Mr. Biden said he expected European allies to contribute more as well.

By comparison, the Pentagon last year estimated that the total war-fighting costs in Afghanistan from 2001 to 2020 at $816 billion, or about $40.8 billion a year. (That did not count non-Defense Department expenditures, and private studies have put the total cost higher.)

Without waiting for the latest aid plan, Congress moved on Thursday to make it easier for Mr. Biden to funnel more arms to Ukraine right away. The House voted 417 to 10 to invoke the Lend-Lease Act of 1941 to authorize Mr. Biden to speed military supplies to Ukraine. The Senate passed the legislation unanimously earlier this month, meaning it now moves to Mr. Biden’s desk for his signature.

The original act, proposed by Franklin D. Roosevelt, authorized the president to lease or lend military equipment to any foreign government “whose defense the president deems vital to the defense of the United States” and was used originally to aid Britain and later the Soviet Union in their battle against Nazi Germany.

“Passage of that act enabled Great Britain and Winston Churchill to keep fighting and to survive the fascist Nazi bombardment until the United States could enter the war,” said Representative Jamie Raskin, Democrat of Maryland. “President Zelensky has said that Ukraine needs weapons to sustain themselves, and President Biden has answered that call.”

The legislation targeting oligarchs would streamline ongoing efforts to find and confiscate bank accounts, property and other assets from the Russian moguls.

Among other things, it would create a new criminal offense for possessing proceeds from corrupt dealings with the Russian government. It would also add the crime of evading sanctions to the definition of “racketeering activity” in the Racketeer Influenced and Corrupt Organizations Act, known as RICO.

Reporting was contributed by Marc Santora from Krakow, Poland; Jeffrey Gettleman and Maria Varenikova from Kyiv, Ukraine; Emily Cochrane, Catie Edmondson, Eric Schmitt and Michael D. Shear from Washington; Ivan Nechepurenko from Tbilisi, Georgia; Shashank Bengali and Matthew Mpoke Bigg from London; and Farnaz Fassihi from New York.