As President Donald Trump looks to fulfill what he says is his goal to be known as a "peacemaker" by settling the war in Ukraine, he's called for a direct line of communication with Russia's President Vladimir Putin multiple times during the first days of his second term -- saying he "really would like to be able to meet" the Russian leader soon to "get that war ended."

"I think from what I hear, Putin would like to see me. We'll meet as soon as we can," Trump said at the White House on Thursday.

The Kremlin said that Putin was ready to hold a call with Trump and was only waiting on Washington to signal that Trump was also ready.

Both sides have indicated that a phone call is seen as a first step toward a more substantial, in-person meeting between the leaders -- a format Putin suggested he would prefer.

"It would be better for us to meet, based on the realities of today, to talk calmly on all those areas that are of interest to both the United States and Russia," Putin said during a televised interview on Friday.

Breaking the silence

Any conversation between the two would mark the first time a sitting U.S. president and Putin have spoken since the war in Ukraine began, although former President Joe Biden held phone calls with Putin multiple times in the leadup to Moscow's invasion to urge Putin against it.

Communication between lower tiers of government has continued through the war, and a source familiar with the situation told ABC News that working-level talks between American and Russian diplomats had continued at normal clip following Trump's inauguration.

Even before Trump reentered the White House, his national security adviser, Mike Waltz, said in an interview on ABC's "This Week" that preparations were already underway for Putin and Trump to speak by phone "in the coming days and weeks."

Trump also said he would take it further than a phone call, predicting he would meet with Putin "very quickly" after his inauguration.

Putin has also seemed receptive reopening lines of communication with the White House, applauding Trump's willingness to "restore direct contacts with Russia" earlier this week.

At times, Trump has been criticized for having what some describe as an overly cozy relationship with Putin.

In February 2022, Trump praised Putin's strategy in Ukraine, calling the invasion "genius" and "savvy" during a radio interview.

At a summit with Putin held in Helsinki in 2018, Trump drew bipartisan criticism for saying he "didn't see any reason to believe" Russia meddled in the 2016 election, contrary to the findings of the U.S. intelligence community.

Putin has also spoken highly of Trump, endorsing his baseless claims that the 202 election was stolen from him and agreeing with Trump's statements that the war in Ukraine never would have happened if were still in office.

Pressure tactics

Trump's track record of warm relations with Putin sharply contrasts with his recent threats against Russia.

"Settle now, and STOP this ridiculous War! IT'S ONLY GOING TO GET WORSE. If we don't make a 'deal', and soon, I have no other choice but to put high levels of Taxes, Tariffs, and Sanctions on anything being sold by Russia to the United States, and various other participating countries," Trump wrote on Truth Social earlier this week.

In the wake of the war in Ukraine, trade between the U.S. and Russia plummeted to the lowest levels since the fall of the Soviet Union -- making Trump's threat of tariffs mostly toothless.

However, during a virtual appearance at the World Economic Forum in Davos, Switzerland, the president upped the ante, saying he would ask the OPEC cartel to "bring down the cost of oil."

"That will end the war. You could end the war," he said.

The Biden administration, along with other governments in the G7, instituted a $60 per barrel price cap on Russian oil exports shipped by sea in 2022 -- a play to eat into Moscow's profits while avoiding an energy crisis.

Moscow has been able to make a small profit from its discounted exports, but if OPEC were to ramp up production of oil, therefore bringing down the cost of gas from other exporters, the Kremlin could lose its customers.

"If Trump can persuade OPEC to boost production at the expense of Russian volumes -- a deal his predecessor was never able to strike -- he could secure leverage over Moscow, maintain low world energy prices, and keep US oil and gas companies and their customers happy," said Joseph Webster, a senior fellow at the Atlantic Council's Global Energy Center.

For its part, the Kremlin has responded to Trump's threats cooly.

"We do not see any particular new elements here," spokesperson Dmitry Peskov said on Thursday.

Other issues, other countries

Beyond Ukraine, both Trump and Putin have indicated that they intend to intend to resume talks on nuclear arms control.

Russia and the U.S. control 88% of the world's nuclear warheads, but through the course of the war in Ukraine, both countries have suspended their participation in the last major arms control treaty between the two powers, which is due to expire in 2026.

"Negotiating any new nuclear arms control agreement with the Kremlin would be difficult to hammer out and a new comprehensive framework deal could require sustained talks over many months, if not years, to achieve," said Daryl Kimball, executive director of the Arms Control Association.

During Trump's first term in office, he aimed but failed to strike a three-way nuclear nonproliferation deal between the U.S., Russia and China -- a prospect Trump has revisited during the first days of his second term.

When it comes to ending the war in Ukraine, Trump has also said he intends to bring China -- Russia's most powerful ally -- into the fold, saying Beijing has a "great deal of power over the situation."

What's not clear is how -- or if -- Trump plans to incorporate Ukraine in the talks.

In an interview with Fox News that aired on Thursday, Trump criticized Ukraine's President Volodymyr Zelenskyy -- saying "he's not angel" and that he "shouldn't have allowed" the war with Russia to happen.

On Friday, Andriy Yermak, the head of the Office of the President of Ukraine, wrote on social media that Putin " is trying to push the idea of negotiations with the United States."

"But he has one condition: he wants to decide Europe's fate -- without Europe. And he seeks to talk about Ukraine-- without Ukraine," Yermak said, "This will not happen.