Russian President Vladimir Putin indicated Tuesday that he will not immediately recognize two Russian-controlled breakaway regions in eastern Ukraine as independent.

Putin said he believes the idea has the support of the majority of Russians but that he thinks Russia should continue to try to resolve the conflict with Ukraine through the Minsk peace agreements.

The Minsk accords signed in 2014 and 2015 were aimed at ending the ongoing conflict between the Ukrainian army and the Russian-backed separatists forces in an area of southeastern Ukraine known as the Donbas. But Putin's recognition of the regions would amount to Russia formally withdrawing from the agreement.

Putin's comments suggest that while he doesn't intend to immediately move to recognize the regions, he might keep the action as a threat hanging over negotiations with Ukraine and the West. He painted the parliament vote as the expression of lawmakers rather than something directed by the Kremlin.

"We must do everything to resolve the problems in Donbas but, as before, starting from the possibilities from the Minsk agreement that have not been realized to their end," Putin said Tuesday.

Meanwhile, the leader of one of the regions welcomed the Russian parliament vote but fell short of calling on Putin to take the step.

"We thank the deputies of the State Duma for the results of today’s vote," Denis Pushilin, head of the self-proclaimed Donetsk People's Republic said in a statement Tuesday. "With that, we will treat with respect and understanding any decision taken by the top leadership of the Russian Federation."

Pushilin called the initiative "timely," given what he claimed was the threat from Ukraine, which he alleged was massing troops near the regions and showed Kyiv has no intention of fulfilling the Minsk agreements or resolving the conflict peacefully.

-ABC News' Patrick Reevell

The United States is assessing Russia's claim that it is withdrawing some troops from Ukraine's borders, U.S. Ambassador to NATO Julianne Smith said Tuesday.

During a press briefing at NATO headquarters in Brussels, Smith cast some doubt on the claim after Russia made similar statements in late December.

"All I can say is we'll have to verify that and take a look," Smith told reporters. "We want to make sure we understand what they're talking about when they say de-escalation, and we want to verify that that is in fact what's happening. So stand by, we'll obviously take a look at that."

When asked again whether some Russian forces were in fact pulling back, Smith reiterated: "I can't say yes or no. I can't say really anything about it at this moment because this is something that we'll have to look at closely and verify in the days ahead."

NATO's defense ministers, including U.S. Secretary of Defense Lloyd Austin, will meet Wednesday to discuss deployments within the military alliance and a "variety of contingencies," according to Smith, who noted that NATO "will continue to determine whether or not additional enhancements might be necessary."

While any Russian troop withdrawals could be a sign of de-escalation, the law passed Tuesday in Russia's parliament calling on President Vladimir Putin to recognize Russian-controlled breakaway regions in eastern Ukraine as independent would be a "new shift in the escalation," Smith said, adding that the U.S. and NATO "would monitor that very closely" and determine its response.

"If they proceed with this, then I think it's a clear violation of Ukraine's territorial integrity and its sovereignty, and it's also a violation of the Minsk agreement," she told reporters, "and so that would obviously be a new shift in the escalation."

As the U.S. and NATO await Russia's written proposals on issues like arms control and military exercises, Smith again called on Russia to engage meaningfully in talks.

"Look, we can spend the rest of the year going back and forth exchanging letters," she said, "but really what's important is the best way to proceed would be for us to sit down at the table again."

Until then, Smith said they do not know what Putin will decide.

"We do not understand fundamentally -- none of us do -- what is inside President Putin's head," she added, "and so we cannot make any guess about where all of this is headed."

-ABC News' Conor Finnegan

NATO Secretary-General Jens Stoltenberg said Tuesday that the military alliance has "not seen any signs of reduced Russian military presence on the borders of Ukraine."

"So far, we have not seen any de-escalation on the ground," Stoltenberg told reporters at NATO headquarters in Brussels. "But we will continue to monitor and to follow closely what Russia is doing, and the signs coming from Moscow about a willingness to continue to engage in diplomatic efforts -- that gives some reason for cautious optimism. But we will, of course, follow very closely what's happening on the ground and whether this is reflected in some real de-escalation of the Russian military build-up in and around Ukraine."

Top cybersecurity officials from the U.S. Department of Homeland Security and the FBI have warned of potential attacks on American cyber infrastructure in concert with a physical invasion of Ukraine, according to a source familiar with the matter.

The source told ABC News that the warning came Monday on a call with state and local officials -- but it's not new. On Friday, the Homeland Security Department's Cybersecurity and Infrastructure Security Agency (CISA) explicitly warned of Russian cyberattacks and made a veiled mention of the ongoing geopolitical climate.

"The Russian government has used cyber as a key component of their force projection over the last decade, including previously in Ukraine in the 2015 timeframe," CISA said in an online post. "The Russian government understands that disabling or destroying critical infrastructure—including power and communications—can augment pressure on a country’s government, military and population and accelerate their acceding to Russian objectives."

U.S. officials have said a Russian invasion of Ukraine could happen "at any time" and that they believe Ukraine could also be a target of an offensive cyberattack. Ukraine has already been the target of what some Ukrainian officials believed was a Russian cyberattack earlier this year, when suspected Russian hackers defaced Ukrainian government websites.

The U.S. Department of Homeland Security has been warning in bulletins as early as January that there could be a cyberattack tied to a possible Russian invasion.

-ABC News' Luke Barr