Russia has made two overtures to ease tensions around Ukraine: Reporting a pullback of troops near its neighbor and welcoming talks with the West. But the United States and its allies said they needed evidence of the troop movements, claiming that the threat of a Russian invasion still looms large.

For the second day Tuesday, there were signs of hope that Europe might avoid war following weeks of escalating East-West tensions as Moscow massed around 150,000 troops on three sides of Ukraine and held massive military drills. Those moves led to dire warnings from Washington, London and other European capitals that Russia was preparing to roll into Ukraine.

But the tenor changed this week. President Vladimir Putin said Tuesday that Russia does not want war and would rely on negotiations in its efforts to eliminate any chance that Ukraine could one day join NATO – his key demand in the crisis. At the same time, he did not commit to a full pullback, saying Russia’s next moves in the standoff will depend on how the situation evolves.

Russia also offered few details of the pullback, and President Joe Biden said American officials had not verified Russia’s claim. He promised that the U.S. would give diplomacy "every chance," but he struck a skeptical tone about Moscow's intentions.

"Two paths are still open," Biden said in remarks at the White House. "But let there be no doubt: If Russia commits this breach by invading Ukraine, responsible nations around the world will not hesitate to respond. If we do not stand for freedom where it is at risk today, we’ll surely pay a steeper price tomorrow."

Even amid the glimmers of hope, Biden said 150,000 Russian forces are now massed near Ukraine and in neighboring Belarus – an increase from an earlier U.S. estimate of 130,000 troops.

Russia’s claim that it pulled back troops "would be good, but we have not yet verified that," Biden said. "Indeed, our analysts indicate that they remain very much in a threatening position."

Russia has denied having any invasion plans. It wants the West to keep Ukraine and other former Soviet nations out of NATO, halt weapons deployments near Russian borders and roll back forces from Eastern Europe.

The U.S. and its allies have roundly rejected those demands, but they offered to engage in talks with Russia on ways to bolster security in Europe.

Speaking after meeting with German Chancellor Olaf Scholz, Putin said the West agreed to discuss a ban on missile deployment to Europe, restrictions on military drills and other confidence-building measures – issues that Moscow put on the table years ago.

He said Russia is open to discussing "some of those elements" but added that it would do so only in combination "with the main issues that are of primary importance for us."

While Scholz reiterated that NATO's eastward expansion "is not on the agenda – everyone knows that very well," Putin retorted that such assurances would not assuage Moscow.

"They are telling us it won't happen tomorrow," Putin said. "Well, when will it happen? The day after tomorrow? What does it change for us in the historic perspective? Nothing."

Scholz also said diplomatic options are "far from exhausted," and he praised the announcement of a troop withdrawal as a "good signal," adding: "We hope that more will follow."

The Russian Defense Ministry released images of tanks and howitzers rolling onto railway platforms and more tanks rolling across snowy fields. It did not disclose where or when the images were taken or where the vehicles were headed, other than "to places of permanent deployment."

Ukraine expressed skepticism.

"We won’t believe when we hear, we’ll believe when we see," Ukrainian Foreign Minister Dmytro Kuleba said.

On Wednesday, Russia said military drills in Moscow-annexed Crimea had ended and that soldiers were returning to their garrisons, a day after it announced a first troop pullback from Ukraine's borders.

"Units of the Southern Military District, having completed their participation in tactical exercises, are moving to their permanent deployment points," Moscow's defense ministry said in a statement, as state television showed images of military units crossing a bridge linking the Russian-controlled peninsula to the mainland. The statement said tanks, infantry vehicles and artillery were leaving Crimea by rail.

Western allies were also skeptical of Moscow's announcement of a troop withdrawal from the Ukrainian border. Germany and Spain have expressed concern, saying they need proof that Russian troops are indeed outside neighboring borders. German Foreign Minister Annalena Baerbock has given a cautious response to an announcement from Russia about a partial pullback of troops from areas near the Ukrainian border.

"Every genuine step to de-escalate the situation is a reason for hope," Baerbock said on Tuesday during a visit to Spain. The announcements from the Russian side need to be carefully verified, she added. Her Spanish counterpart, Jose Manuel Albares, said that if the move does result in a Russian pullback, it would be "excellent news."

Western military analysts said they needed more information to judge the significance of the latest troop movements.

"One should maintain an air of cautious skepticism," said Henry Boyd of the International Institute for Strategic Studies in London. "There have been past discrepancies between Russia's official announcements and its actions on the ground."

Many of the Russian forces in Belarus for drills due to end on Sunday have come from thousands of miles away in Russia's central and eastern military districts.

Rob Lee, a military analyst specializing in Russia, said the announcement was "potentially good news," but it was important to see where those forces went after the culmination of joint exercises between Russia and Belarus on Sunday.

"As long as that remains nearby, Russia will have the capacity to conduct a significant escalation, though possibly not on as short notice," he told Reuters.

NATO's chief welcomed signals from Russia in the past two days that it may be looking for a diplomatic solution but urged Moscow to demonstrate its will to act.

"There are signs from Moscow that diplomacy should continue. This gives grounds for cautious optimism. But so far, we have not seen any sign of de-escalation on the ground from the Russian side," NATO Secretary-General Jens Stoltenberg told reporters. He said Russia often left military equipment behind after exercises, creating the potential for forces to regroup.

Britain has thus far not seen any evidence that Russia is withdrawing troops from positions near the Ukrainian border, Defence Secretary Ben Wallace said on Wednesday.

"We haven't seen any evidence at the moment of that withdrawal," Wallace told Times Radio. "Physical observations that we see show the opposite of some of the recent rhetoric coming out the Kremlin," Wallace told the BBC. British Prime Minister Boris Johnson also said there were signs of a diplomatic opening but "the intelligence we're seeing today is still not encouraging."

Meanwhile, a series of cyberattacks knocked out the websites of the Ukrainian army, the defense ministry and major banks. There was no indication that the relatively low-level denial-of-service attacks might be a smoke screen for more serious cyber mischief. White House press secretary Jen Psaki said the U.S. has not yet determined who was behind the attacks.

Despite the worst East-West tensions in decades, few Russians expect a war. In a village in Russia’s Belgorod region, about 30 kilometers (18 miles) from Ukraine’s border, residents carried on with life as usual, even as more military personnel have been passing through village streets.

"We are really on the border, we really have relatives here and there, everyone has somebody" on the Ukrainian side, villager Lyudmila Nechvolod said. "No one wants war."

Russian lawmakers urged Putin to recognize rebel-held areas in eastern Ukraine as independent states. The State Duma, Russia’s lower house, voted to submit an appeal to Putin to that effect.

Putin said the request reflects the Russian public's sympathy for the suffering of people trapped in the conflict in eastern Ukraine that has killed over 14,000 since 2014. He noted, however, that Russia continues to believe a 2015 peace deal brokered by France and Germany should serve as the main vehicle for a settlement of the separatist conflict.