KYIV, Ukraine — Ukraine’s military warned on Friday that the Russian-backed separatist army in the country’s east had been put on a high level of alert, completing a near encirclement of Ukraine by forces now poised for military action, even as the Biden administration warned that a Russian invasion could be imminent.

The drills tested the separatists’ preparation for live-fire operations, practicing “driving artillery, tanks and armored vehicles” in field exercises, the Ukrainian statement said. Some units of the force, believed to number 30,000 troops, were put on their highest level of alert, the Ukrainians said, and senior Russian military officers were observing the activity.

The warning coincided with an even more dire pronouncement out of Washington, where officials said that Russia had moved up its timetable and could launch an invasion of Ukraine within a matter of days, even before the end of the Olympics.

“Russia could choose in very short order to commence a major military action against Ukraine,” the national security adviser, Jake Sullivan, said. But officials also cautioned that they could not yet be sure exactly when, or even if, Mr. Putin may decide to invade.

Adding to the sense of foreboding, numerous countries — including the United States, Britain and even Russia — issued urgent warnings to their citizens to leave Ukraine immediately. President Biden said that in the event of a war, U.S. troops would not be able to assist in an evacuation. Many others began evacuating embassy staff.

The assessment from Kyiv was the latest evidence of a shift by officials there to more alarming commentary about the military risk facing the country. That follows weeks of efforts to minimize the threat of an invasion, seeking to calm the public, limit the economic fallout and avoid anything that could be deemed a provocation by Moscow.

Ukraine this week began its own nationwide military exercises to coincide with joint Russian and Belarusian exercises to the north of Ukraine, in Belarus, only 140 miles from Kyiv, the Ukrainian capital.

Those joint exercises involved a flurry of military activity on Friday, the Russian Ministry of Defense said in a statement. Troops practiced evacuating the wounded from the battlefield, maneuvering with armored vehicles and reconnaissance activities. Russia’s Air Force jets fired at an airborne target.

To the south, the Russian Navy announced on Thursday the closure of large swaths of the Black Sea for live-fire exercises by its fleet that will effectively blockade Ukrainian ports, including the port of Odessa. The naval exercises were scheduled to begin Sunday and last six days.

Russia has massed armored vehicles and soldiers near its borders to the northeast of Ukraine and in the south on the Crimean Peninsula, which Moscow annexed in 2014, as well as in Belarus.

On Friday, President Biden held a phone call with 10 other trans-Atlantic leaders “to discuss our shared concerns about Russia’s continued buildup of military forces around Ukraine and continued coordination on both diplomacy and deterrence,” the White House said in a statement.

Among those scheduled to join Mr. Biden were President Ursula von der Leyen of the European Commission, European Council President Charles Michel, President Emmanuel Macron of France, Chancellor Olaf Scholz of Germany, the NATO Secretary General Jens Stoltenberg and Prime Minister Boris Johnson of Britain.

A wide range of diplomatic efforts to defuse the crisis have borne little fruit to date, amid growing signs Friday that the situation is deteriorating.

Germany’s foreign minister, Annalena Baerbock, said that “we are not seeing de-escalation” by Russia despite multiple diplomatic overtures. The U.S. secretary of state, Antony J. Blinken, said during a visit to Australia that “we continue to see very troubling signs of Russian escalation, including new forces arriving at the Ukrainian border.”

A meeting in Moscow on Friday between the British defense secretary, Ben Wallace, and his Russian counterpart, Sergei K. Shoigu, was cordial but led to a dim assessment of relations between Russia and the West by Mr. Shoigu.

After Mr. Wallace laid a wreath at the Tomb of the Unknown Soldier in Moscow, acknowledging Russia’s loses in World War II, Mr. Shoigu nodded to the countries’ alliance in that war but added: “Unfortunately, the level of our cooperation is close to zero and is about to cross the zero meridian and reach the negatives.”

In news conferences that extended into early Friday morning in Berlin, both Russian and Ukrainian negotiators said a channel of talks supported by President Emmanuel Macron of France had brought no breakthroughs.

The negotiations focused on a settlement agreement for the eastern Ukraine war but were seen as a possible path to ease the wider tensions from the Russian buildup. They were the second effort this year by foreign policy advisers to the French, German, Russian and Ukrainian governments.

“It would be good if during the second meeting we could agree on something,” Andriy Yermak, Ukraine’s chief negotiator, said. After nine hours of talks the negotiators could not agree on a joint statement. “It went the way it did today,” Mr. Yermak said.

Russia’s negotiator, Dmitri Kozak, offered an even more dour assessment. He said the Ukrainian government had not altered its longstanding positions in the settlement talks for the eastern Ukraine conflict, which have been going on for seven years.

Separate talks in Moscow on Thursday between the British foreign secretary, Liz Truss, and Russia’s foreign minister, Sergey L. Lavrov, also went nowhere, with Mr. Lavrov comparing them to “the conversation of a mute person with a deaf person.”

Ms. Truss had said one purpose of the visit was to convey to Russian officials warnings about the seriousness of Western economic sanctions and other repercussions if they use military force in Ukraine. Mr. Lavrov countered by reiterating Russia’s position that it has no plans to invade Ukraine and that its military is merely conducting exercises.

Turkey’s president, Recep Tayyip Erdogan, has offered to mediate, a proposal accepted by Ukraine but declined by Russia. Next week, the German chancellor, Olaf Scholz, is scheduled to visit Kyiv and Moscow. And Russian officials have said they will respond in writing to proposals for security talks offered by the United States and NATO.

Russia has made a series of demands of the West, including scaling back the NATO military presence in Eastern Europe to 1990s levels and guaranteeing that Ukraine could never join NATO. The United States has called those demands “non-starters’’ and instead offered a series of proposals aimed at arms control.