The official county-by county of Michigan is in, and it shows President-elect Donald Trump did what he set out to do, picking off the battleground prize and winning it by nearly 11,000 votes.

Earlier counts had the Republican ahead by about 13,000 votes. But in final county-by-county votes posted by state election officials Wednesday, Trump's official lead narrowed to 10,704, the Detroit Free Press reported.

Clinton picked up her biggest share of votes in the canvass in Wayne County, which includes Detroit, gaining 565 votes.

Trump won with 47.59 per cent of the vote, compared to Clinton's 47.35 per cent of the vote.

The narrow win vindicates Trump's claims throughout the race that he could compete in rust belt Democratic strongholds like Michigan. Trump made it his mission, stressing trade and job losses to overseas competitors, to bring back some of the 'Reagan Democrats' in Macomb County and other working class areas.

President-elect Donald Trump won Michigan by 10,704 votes, according to final results posted by the Michigan secretary of state

Democrats mostly dismissed the idea throughout the general election, although in the final days of the campaign Clinton rushed to Grand Rapids and Detroit, and dispatched President Obama to Ann Arbor in a futile effort to stave off the upset.

With Michigan in his column, Trump won 306 electoral votes, to Clinton's 232, a convincing electoral win. But Clinton has amassed a 2 million vote lead in the popular vote – the second time since 2000 where the Democrat got more votes but lost the White House anyway.

Trump also seized two other Democratic prizes by winning Pennsylvania and Wisconsin.

Green Party presidential candidate Jill Stein is raising funds to call for a recount in the three states.

PHOTO FINISH: Donald Trump beat Hillary Clinton by just 10,704 votes, according to the final tally released by the secretary of state

The official loss of Michigan doesn't change the outcome. Hillary Clinton was already trailing there, and Trump had amassed enough electoral votes to win without he state

Green Party candidate Jill Stein has raised enough funds to seek a recount in three states, including Michigan

She announced that she has raised the necessary $2 million to pay for recounts in Wisconsin, Michigan and Pennsylvania after experts said it was possible that hackers had artificially lowered Hillary Clinton's counts there.

She had reached $3.5 million by Thursday.

'We deserve elections we can trust,' said Stein's campaign said, adding that the effort was not intended to help Clinton.

Computer scientists including J. Alex Halderman, the director of the University of Michigan Center for Computer Security and Society, have conducted an analysis of the vote.

That vote showed that Clinton performed 7 per cent worse in Wisconsin counties that have electronic voting machines than in counties that relied on paper ballots that are logged with an optical scanner.

The group have contacted high level Clinton staffers, including campaign chair John Podesta and general counsel Marc Elias, and made their case in a conference call, according to New York Magazine.

The Clinton camp hadn't provided comment about the activists' push to call for a recount of the vote.

Although the scientists provide no evidence of a hack, they note that computer vote tallying machines in closely contested states could be susceptible to hacking – in an election that featured hacks of the Democratic National Committee and of Podesta's private email account.