Russian President Vladimir Putin has become one of the last world leaders to congratulate US President-elect Joe Biden on his victory.
The Kremlin had said it would wait for official results from November’s vote before recognising the victory.
The Democrat won November’s contest with 306 electoral college votes to the Republican incumbent’s 232.
Mr Trump still refuses to concede, making unsubstantiated claims of widespread fraud.
Confirmation by the electoral college was one of the steps required for Mr Biden to take office.
In a blow to Mr Trump, one of his main Republican allies, Senate Majority Leader Mitch McConnell, congratulated Mr Biden on Monday.
Most world leaders congratulated him within days of the 3 November poll, when it was clear he had defeated Mr Trump.
Mr Biden and Mr Putin had frosty relations when the former served as vice-president under Barack Obama.
Mexican President Andrés Manuel López Obrador has also finally congratulated Mr Biden but Brazil’s President, Jair Bolsonaro, has still not done so, nor has North Korea’s Kim Jong-un.
What did Putin say in his message to Biden?
According to a Kremlin statement, Mr Putin wished Mr Biden every success and said he was “ready for collaboration and contacts with you”.
He “expressed confidence that Russia and the United States, which have a special responsibility for global security and stability, could, despite their differences, really help to solve the many problems and challenges facing the world”, the statement added.
But analysts say the President-elect, who describes Mr Putin as an autocrat, is expected to take a tougher line on Russia than Mr Trump.
Russia has faced accusations of interference in the 2016 US election to help get Mr Trump elected.
While Mr Putin waited nearly a month and a half before congratulating Mr Biden, in 2016 he congratulated Mr Trump on his victory the day after the vote.
What did McConnell say?
Speaking on the Senate floor, Mr McConnell said: “Today I want to congratulate President-elect Joe Biden.”
Also congratulating Kamala Harris, he added: “All Americans can take pride that our nation has a female vice president-elect for the very first time.”
Senate Democratic Leader Chuck Schumer urged Mr Trump to “end his term with a modicum of grace and dignity”.
“For the sake of our democracy, for the sake of peaceful transition of power, he should stop the shenanigans, stop the misrepresentations and acknowledge that Joe Biden will be our next president,” he said.
It took more than a month, but Mitch McConnell is now acknowledging the obvious – that the former Vice President will be the next US president.
