President Trump is willing to visit Moscow, the White House said Friday, hours after Russian President Vladi­mir Putin said Trump “has such an invitation.”

The statement comes as Trump’s apparent eagerness to embrace Putin is coming under increasing scrutiny after the summit between the two leaders last week in Helsinki.

“President Trump looks forward to having President Putin to Washington after the first of the year, and he is open to visiting Moscow upon receiving a formal invitation,” White House press secretary Sarah Huckabee Sanders said in a statement.

On Wednesday, the White House announced that a planned follow-up meeting between Trump and Putin in Washington, originally expected to take place this fall, will instead be pushed to next year.

Putin said Friday that he was prepared to visit Trump in Washington and that he had also invited the president to Moscow. Either way, Putin said, the timing for such a visit had to be right — an apparent reference to White House claims that the next Putin-Trump summit needs to wait until after the conclusion of special counsel Robert S. Mueller III’s probe into Russian interference in the 2016 presidential campaign.

“By the way, he has such an invitation. I told him about this,” Putin said at a news conference at an international summit in Johannesburg on Friday, referring to the possibility of a Trump visit to Moscow. “I’m also prepared to come to Washington, but, I’ll repeat, only if the appropriate conditions are created there.”

Putin said he and Trump have important matters to discuss, including Iran, the war in Syria, and the looming expiration of the New Start nuclear arms control treaty in 2021. He ratcheted up his frequent, public praise of the U.S. president, describing him as a rare politician who keeps his campaign promises. In the past, Putin has noted that those promises included better ties with Russia.

“After elections, some leaders generally quickly forget what it was they promised the people during their campaign,” Putin said. “Trump doesn’t.”

The White House has taken steps in recent days to tamp down on the concerns over the United States’ Russia policy sparked by the Helsinki summit, where Trump appeared to side with Putin and cast doubt on the U.S. intelligence community’s conclusion that Russia interfered in the 2016 presidential election. Trump has since walked back his remarks.

On Friday afternoon, Trump will convene a National Security Council meeting devoted to the issue of election security.

In testimony before the Senate Foreign Relations Committee on Wednesday, Secretary of State Mike Pompeo said Trump “has a complete and proper understanding of what happened” in 2016.

Anton Troianovski reported from Moscow.