Mr Obama also criticised Republican officials for giving oxygen to the outgoing president’s so far baseless claims of widespread voter fraud.
He suggested that the GOP figures publicly backing Mr Trump’s efforts to overturn the election result are only doing so because they are afraid of the president.
The comments were broadcast hours after Rudi Giuliani, Mr Trump’s lawyer, held a press conference in Washington DC, where his team spewed out more basless claims about ballot irregularity.
“These are just bald assertions, they have been repeatedly rejected by the courts,” Mr Obama said of the president’s key battleground state lawsuits.
“I’m less surprised by Donald Trump doing this, he has shown, you know, only a flimsy relationship with the truth,” he told MSNBC contributor Jonathan Capehart.
Despite Mr Trump losing the election by 74 electoral college votes, only a handful of GOP lawmakers are recognising Joe Biden as president-elect.
Capitol Hill observers say the rest refuse to do so publicly for fear of retribution by Mr Trump, whose supporters were key in helping many of them hang onto their seats.
That view was echoed by Mr Obama, who said those rowing in behind the president did so “not because they actually believe it, but because they feel intimidated by it.”
Despite the president’s false claims that he won the election, Mr Obama said “Joe Biden is going to be the next president of the United States”. “Kamala Harris is going to be the next vice president”, he added.
Earlier on Thursday, an undeterred and sweating Mr Giuliani addressed reporters from the Republican National Committee headquarters in Washington D.C.
His team set out its case for widespread voter fraud but failed to provide any evidence – almost two weeks after Mr Biden was declared the election winner.
Instead, the team issued a series of false claims and misleading statements about ballot counting in Michigan and Pennsylvania.
Attorney Sidney Powell, part of the president’s “elite strike force”, offered perhaps the wildest of those allegations.
She claimed that vote counting machines made by the election technology company, Dominion, has ties to the Clinton Foundation and George Soros, the financier, philanthroptist and Democrat donor of Jewish descent.
Ms Powell also claimed to have dentified “massive influence of communist money through Venezuela, Cuba and likely China in the interference with our elections here in the United States”.
While the president’s most loyal minions continued getting their hands dirty, Mr Biden was confirmed the winner in Georgia after a recount, becoming the first Democrat to win the traditionally red state since Bill Clinton in 1996.
Georgia secretary of state, Brad Raffensperger, said there was no evidence of rigging or voter fraud.
“The recount process simply reaffirmed what we already knew: Georgia voters selected Joe Biden to be their next president,” said Jaclyn Rothenberg, the Biden campaign spokeswoman.