Clinton agrees to take part in vote recount across three key states

For Mr Trump’s victory in the presidential race to be overturned all three states would have to be reassigned to Mrs Clinton. Such an outcome was dismissed by the White House, which backed Mr Trump’s legitimacy as the president-elect.

A spokesman for the Obama administration suggested that raising questions about the integrity of the process was playing into Russian hands. He said the Kremlin had probably hoped to raise such doubts through its hacking attacks during the election, including on the Democratic National Committee email system.

The spokesman said: “We stand behind our election results, which accurately reflect the will of the American people. We are confident in the overall integrity of electoral infrastructure and we believe our elections were free and fair from a cybersecurity perspective.”

Mr Trump last night called the bid for a recount a “scam”. Kellyanne Conway, Mr Trump’s campaign manager, called the Clinton campaign a “pack of sore losers”. She told Bloomberg: “After asking Mr Trump and his team a million times on the trail ‘will he accept the election results?’ it turns out Team Hillary and their new best friend Jill Stein can’t accept reality.”

Mr Trump won Michigan by 10,704 votes, Pennsylvania by 70,010, and Wisconsin by 27,257 votes. His lead in Michigan was just 0.3 per cent and the result has not yet been officially certified. The deadline for Miss Stein to apply for a recount in Michigan is Wednesday. Mr Trump will then have seven days to object and the election board will make a decision.

The deadline for applying in Pennsylvania passed a week ago but that can be overturned in court. Miss Stein’s deadline for doing that is tomorrow.

Miss Stein needed to raise $7 million (£5.6million) for application and legal costs and by yesterday morning had reached $5.7 million. She said there was a need to “shine a light on just how untrustworthy the US election system is”.

According to one group of computer scientists Mrs Clinton’s votes were seven per cent lower than expected in counties that used electronic machines to tally votes. They said it was unlikely cyber attacks were responsible, but the only way to be sure was to examine the ballots and electronic equipment.