Mr Ryan, a former speaker of the House of Representatives, said the US president should “embrace” the transition process because “the election is over," as he addressed the Bank of America’s virtual European Credit Conference on Tuesday.
His remarks came after Mr Trump’s said on Monday night that the federal agency responsible for the presidential transition process, the General Services Administration (GSA), should "do what needs to be done” but continued to refuse to concede the election.
Mr Ryan argued that allowing the GSA to facilitate the transition process for Joe Biden’s team was not enough and condemned the president’s legal team for undermining American democracy with “baseless conspiracies” of election fraud.
“Frankly, I really think it’s in the president’s best interest to acknowledge these things and not just have the GSA technically facilitate the transfer of power, but to embrace the transfer of power, the system we have,” said Mr Ryan, as reported by Politico.
The Republican party’s 2012 vice-presidential nominee said baseless allegations about the election outcome were “doing damage to our country, to our democratic institutions and norms.”
“These legal challenges to the outcome and the attacks on our voting system really need to stop, in my opinion," Mr Ryan said. “The outcome will not be changed.
“So, the election is over. The outcome is certain, and I really think the orderly transfer of power - that is one of the most uniquely fundamental American components of our political system,"
Mr Trump claimed earlier this week he “will never concede” to Mr Biden, while his legal team continued to advance conspiracies about the election amid faltering legal challenges.
Mr Ryan said “these sort of baseless conspiracy theories” were clearly unfounded.
He is the latest of several Republican politicians to break ranks and urge Mr Trump to admit defeat, after Pennsylvania senator Pat Toomey congratulated Mr Biden on his victory and former New Jersey governor Chris Christie describing the president’s legal team as a “national embarassment”.