A vote recount has confirmed Donald Trump's presidential election win in the state of Wisconsin.

It was announced on Monday that the Republican candidate had defeated Democrat Hillary Clinton by more than 22,000 votes, the same number recorded in the original count.

Three million votes cast statewide were re-examined at the request of Green Party candidate Jill Stein, but the immense undertaking yielded a change of just 0.06 per cent, with the President-elect picking up an extra 162 votes.

The audit was finalised on the same day a federal judge rejected a Green Party-backed request to recount paper ballots in Pennsylvania's presidential election and scan some counties' election systems for signs of hacking.

Ms Stein, who paid for the Wisconsin recount by raising $7 million from grass-roots donors, has had several attempts to instigate similar statewide recounts in Pennsylvania and Michigan blocked by the courts.

Her request to have every vote checked by hand in Wisconsin, which was backed by Ms Clinton, was also rejected.

In a statement on Monday, Ms Stein thanked the state’s election employees for working to complete the recount by the Tuesday deadline mandated by the federal government to resolve any election disputes. But she also said that the refusal of some counties to conduct a hand recount of ballots left many questions unanswered about the integrity of the process.

“This recount was never about changing the outcome; it was about validating the vote and restoring confidence in our voting system to Americans across the country who have doubts. The recount in Wisconsin raised a number of important election integrity issues that bear further assessment and serious action to ensure we have integrity and confidence in our electoral system,” she said in a statement.

A lawsuit filed by Ms Stein’s campaign alleged there had been irregularities in Wisconsin’s vote totals that “indicate potential tampering with electronic voting systems".

Ms Stein, who got about 1 per cent of the vote in each of the states Mr Trump narrowly won, argued that voting machines in all three states were susceptible to hacking.

In Pennsylvania, US District Judge Paul Diamond said there were at least six grounds that required him to reject the Green Party's lawsuit, which had been opposed by Mr Trump, the Pennsylvania Republican Party, and the Pennsylvania attorney general's office.

Suspicion of a hacked Pennsylvania election “borders on the irrational” and granting the Green Party's recount bid could “ensure that no Pennsylvania vote counts”, given Tuesday's federal deadline to certify the vote for the Electoral College, wrote Mr Diamond, an appointee of former Republican President George W. Bush.

“Most importantly, there is no credible evidence that any 'hack' occurred, and compelling evidence that Pennsylvania's voting system was not in any way compromised,” Mr Diamond wrote. He also said there had been an “unexplained, highly prejudicial” wait by the Green Party before filing the lawsuit, four weeks after the 8 November election.

The Green Party has hit numerous barriers in county and state courts as it has sought to have votes recounted.

A lawyer for the Green Party said Monday they were disappointed and unable to immediately say whether they would appeal the decision in Pennsylvania.

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“But one thing is clear,” said the lawyer, Ilann Maazel. “The Pennsylvania election system is not fair to voters and voters don't know if their votes counted, and that's a very large problem.”

In Pennsylvania, Mr Trump beat Ms Clinton by about 44,000 votes out of 6 million cast.