The United States and Russia bitterly attacked each other over the Ukraine crisis in a diplomatic brawl Monday at the U.N. Security Council, in a session replete with acidic exchanges that could have been lifted from the Cold War era.

The Americans, backed by their Western allies, accused Russia of endangering peace and destabilizing global security by massing more than 100,000 troops on Ukraine’s borders, while Kremlin diplomats dismissed what they called baseless and hysterical U.S. fear-mongering aimed at weakening Russia and provoking armed conflict.

“The situation we are facing in Europe is urgent and dangerous,” the United States ambassador, Linda Thomas-Greenfield, said in her opening remarks to a televised meeting of the Council that Russia had sought to prevent. “Russia’s actions strike at the very heart of the U.N. charter.”

Her Russian counterpart, Vassily Nebenzia, said it was the Americans who were the provocateurs, “whipping up tensions and provoking escalation,” as he insisted that Russia had no plans to invade Ukraine.

“You are almost pulling for this,” he said, looking at Ms. Thomas-Greenfield. “You want it to happen. You’re waiting for it to happen, as if you want to make your words become a reality.”

The meeting of the 15-nation Security Council, requested by the United States last week, had not been expected to produce any diplomatic breakthrough: the Council is known more for its failures to avert armed conflicts rather than success in preventing them.

Still, the meeting represented the highest-profile arena for the two biggest nuclear military powers to sway world opinion over the escalating tensions involving Ukraine.

As diplomats sparred at the United Nations, behind-the-scenes efforts to resolve the crisis accelerated, with President Emmanuel Macron of France speaking to President Vladimir V. Putin of Russia on the phone on Monday for the second time in four days.

The Kremlin said the two leaders had discussed Ukraine as well as Mr. Putin’s demands for “security guarantees” that would include a legally binding halt on NATO expansion to the east. They agreed to stay in touch by phone and to “work promptly on the possibility of holding an in-person meeting,” the Kremlin said.

American officials said Monday they had received a Russian response to Washington’s proposal, made last week, to defuse the Ukraine crisis. But a State Department official would not detail the response, saying the Biden administration did not want to negotiate in public.

On Tuesday morning, the U.S. secretary of state, Antony J. Blinken, is expected to speak by phone with Russia’s foreign minister, Sergey V. Lavrov.

But even as the diplomats at the Security Council emphasized the need for a peaceful resolution, the tone of the rhetoric between the Russian and American envoys suggested the rift between the two sides over Ukraine, and the threat of military force, remained acute.

In Ukraine itself — where many have been unnerved by the constant drumbeat of menacing news about Russian military maneuvers, cyber-sabotage and disinformation — the anxiety has been compounded by hundreds of bogus bomb threats. The threats, possibly instigated by Russia, were meant to sow panic and fear, Ukrainian officials said. The number of fake bomb scares in January, they said, was six times the level of last year.

Ukraine appealed to Moscow to de-escalate the situation.

“Russia several times announced they do not want war,” Dmytro Kuleba, Ukraine’s foreign minister, said in a video briefing for reporters. “Russia can prove those words by immediately decreasing its military, political and economic pressure on Ukraine. It can abandon ideas of destabilizing the situation inside Ukraine with invented protests, cyberattacks and efforts to disrupt normal life.”

The tensions surrounding Ukraine, a former Soviet republic of 44 million that has recently drifted toward the West, have been smoldering since Russia annexed Ukraine’s Crimean Peninsula in 2014 after a Russia-friendly government in Ukraine was ousted.

The tensions have escalated sharply in recent months and brought U.S.-Russian relations to their lowest point since the Cold War ended three decades ago.

The United States and its NATO partners say Russia’s troop deployments to Ukraine’s borders in recent weeks are part of Mr. Putin’s effort to enlarge his country’s sphere of influence in Eastern Europe. The Kremlin has accused the NATO alliance of threatening Russia and has demanded that it never admit Ukraine as a member.

The Biden administration has vowed to respond with crippling economic sanctions on Russia if it invades Ukraine. The White House press secretary, Jen Psaki, elaborated on that threat Monday, saying the administration had developed “specific sanctions packages” to strike at Russian “elites” and leaders “in or near the inner circle of the Kremlin,” should Mr. Putin order an invasion.

The Security Council meeting adjourned after two hours with no action taken. Mr. Nebenzia pointedly left the meeting before it was over, as Ukraine’s ambassador, Sergiy Kyslytsya, was speaking.

Ms. Thomas-Greenfield told reporters afterward that she was disappointed by the Russian response at the meeting.

“We called for this meeting to allow the Russians to give us an explanation of what their actions are,” she said. “They didn’t give us the answers that any of us would have hoped that they would provide.”

Still, the Biden administration said it regarded the meeting as an important display of the resolve of the United States and its allies to confront Russia over the military threat at Ukraine’s borders.

“If Russia is sincere about addressing our respective security concerns through dialogue, the United States and our allies and partners will continue to engage in good faith,” Mr. Biden said in a White House statement. “If instead Russia chooses to walk away from diplomacy and attack Ukraine, Russia will bear the responsibility, and it will face swift and severe consequences.”

The meeting had the Cold War atmospherics of the angry debates that once punctuated Security Council sessions during the tensest faceoffs between the United States and Soviet Union.

Immediately after the Council convened, the Russians lost a procedural challenge to even holding the meeting. Mr. Nebenzia of Russia accused the Americans of fomenting “unfounded accusations that we have refuted.” He said no Russian troops were in Ukraine, questioning the basic premise of a meeting he described as “megaphone diplomacy.”

Ms. Thomas-Greenfield countered that many private diplomatic meetings had been held about Russia’s military buildup and it was “now time to have a meeting in public.” She asked other members how they would feel “if you had 100,000 troops sitting on your border.”

The Council voted to proceed with the meeting, with only Russia and China objecting. Though both are permanent members of the Council, along with Britain, France and the United States, they cannot use their veto powers to block a meeting.

Russia’s military buildup on Ukraine’s borders, Ms. Thomas-Greenfield said, reflected “an escalation in a pattern of aggression that we’ve seen from Russia again and again.” While she emphasized Washington seeks a peaceful outcome, she said that if the Russians invaded Ukraine, “none of us will be able to say we didn’t see it coming.”

Mr. Nebenzia, in his remarks, said the United States and its Western allies had manufactured a crisis to weaken Russia and drive a wedge between it and Ukraine.

He said the United States had been behind the 2014 change of government in Ukraine that had driven a pro-Moscow leadership from power and had installed “nationalists, radicals, Russophobes and pure Nazis.”

Mr. Nebenzia also sought to draw an analogy to the false American evidence of weapons of mass destruction in Iraq that preceded the 2003 U.S.-led invasion of that country, adding that “what happened to that country is known to all.”

He reinforced a Kremlin message that it is the West that has concocted the crisis, despite the massing of Russian troops on Ukraine’s borders. The Russians have also seized on recent complaints by Ukraine’s president, Volodymyr Zelensky, that the Americans are needlessly sowing “panic.”

Mr. Putin, who has not spoken publicly about Ukraine since December, maintained his silence.

Mr. Kuleba, Ukraine’s foreign minister, told reporters that his government was coordinating diplomacy with its allies, partly through a tactic he described as a “parade of visits” by foreign dignitaries to Kyiv — the theory being that Mr. Putin would be less likely to order an attack if a foreign leader were in town.

Just this week, Ukraine plans to host visits by Prime Minister Boris Johnson of Britain, President Recep Tayyip Erdogan of Turkey, Prime Minister Mateusz Morawiecki of Poland, and Prime Minister Mark Rutte of the Netherlands.

Still, Mr. Kuleba cautioned, the string of visits was no guarantee of restraint by Russia, saying: “who knows what is in Putin’s head?”

Rick Gladstone reported from New York and Maria Varenikova reported from Kyiv, Ukraine. Reporting was contributed by Andrew E. Kramer from Kyiv, Anton Troianovsky from Moscow, Aurelien Breeden from Paris and David E. Sanger and Michael Crowley from Washington.