Russian President Vladimir Putin on Thursday congratulated Donald Trump on his election victory and praised the U.S. president-elect's courage during the July assassination attempt.

"His behaviour at the moment of an attempt on his life left an impression on me. He turned out to be a brave man," Putin said at an international forum following a speech in the Black Sea resort of Sochi. It was his first public comment on the U.S. vote.

"He manifested himself in the very correct way, bravely as a man," he added.

Putin also said that Trump's statements "about the desire to restore relations with Russia, to help end the Ukrainian crisis, in my opinion, deserves attention at least."

The Kremlin earlier welcomed Trump's claim that he could negotiate an end to the conflict in Ukraine "in 24 hours" but emphasized that it will wait for concrete policy steps.

Russia launched its all-out invasion of Ukraine nearly three years ago. Since then, U.S. President Joe Biden's administration has been a key ally for Kyiv, providing a flow of weapons and aid to Ukraine and gathering support among Western nations to enact sanctions against Russia.

Trump has been much more critical of U.S. aid to Ukraine and had even praised Putin at the outset of the invasion.

With Trump's win at the polls on Tuesday, his pending return to the White House leaves Ukraine with questions about how its relationship with Washington may change.

"Will he support continued military aid for Ukraine and ... what sort of a diplomatic settlement will he try to impose or support?" Richard Haass, the president emeritus of the Council on Foreign Relations, told ABC News during a recent discussion on foreign-policy expectations for Trump's second term in office.

'I don't know what will happen'

Asked, during a question-and-answer session at the conference in Sochi on Thursday, what he expects from a second Trump administration, Putin said: "I don't know what will happen now. I have no idea."

"For him, this is still his last presidential term. What he will do is his matter," said Putin, who this year began a fifth term that will keep him in power until 2030 and could seek six more years in office after that.

Kremlin spokesman Dmitry Peskov said Thursday that the Kremlin is not ruling out the possibility of contact between Putin and Trump before the inauguration, given that Trump "said he would call Putin before the inauguration."

There has been reporting by U.S. journalist Bob Woodward that suggests the two leaders have talked by telephone on multiple occasions since Trump left office. Trump has refused to say if this is the case.

WATCH | Ukraine and Trump's return to power: 

Ukraine, Russia brace for Trump’s return to the White House

Some Ukrainians are expressing uneasiness that Donald Trump’s U.S. election win could mean an end to the country's support against Russia. Trump has publicly criticized sending Ukraine billions in military aid, and has said he could make a deal to ‘end the war in a day.’

Peskov has emphasized that Moscow views the U.S. as an "unfriendly" country that is directly involved in the Ukrainian conflict. He dismissed arguments that Putin's failure to reach out quickly to Trump could hurt future ties, saying that Moscow's relations with Washington already are at the "lowest point in history" and arguing that it will be up to the new U.S. leadership to change the situation.

The Kremlin's cautious stand reflected its view of the U.S. vote as a choice between two unappealing possibilities. While Trump is known for his admiration of Putin, the Russian leader has repeatedly noted that during Trump's first term, there were "so many restrictions and sanctions against Russia like no other president has ever introduced before him."

Trump's return to power comes after spending four years out of the Oval Office. The 78-year-old is just the second U.S. president to win non-consecutive terms in office. He will also be the first convicted felon to hold the White House.