Milwaukee County is the state's largest, home to the city of Milwaukee, and black people make up about 27 per cent of the population, more than any other county. Dane County is home to the liberal capital city of Madison and the flagship University of Wisconsin campus.
"The people of Wisconsin deserve to know whether their election processes worked in a legal and transparent way," said Wisconsin lawyer Jim Troupis, who is working with the Trump campaign.
"Regrettably, the integrity of the election results cannot be trusted without a recount in these two counties and uniform enforcement of Wisconsin absentee ballot requirements. We will not know the true results of the election until only the legal ballots cast are counted."
Dean Knudson, a Republican member of the Wisconsin Elections Commission, said Trump raised "significant legal questions that have never been adjudicated in Wisconsin."
But a fellow commission member, Democrat Mark Thomsen, said Trump was trying to change the rules of the election after he lost, but only in two counties.
"That's like losing the Super Bowl and then saying 'I want a review of a certain play using different rules than what applied to the rest of the game,'" Thomsen said. "That is the essence of hypocrisy and cheating and dishonesty."
Milwaukee Mayor Tom Barrett, a Democrat, rejected the Trump campaign's assertion that there were any problems in the two counties.
"This is an attack on cities, on minorities, on places that have historically voted Democratic," Barrett said. "Don't let anyone fool you that this is about irregularities."
Trump's campaign said that clerks wrongly added missing information on returned absentee ballots.
But guidance from the Wisconsin Elections Commission, in place since 2016, says that clerks can fix missing witness address components on the envelopes that contain absentee ballots if they have reliable information. That guidance, passed unanimously by the bipartisan elections commission, has been in place for 11 statewide elections without objection.
The elections commission said that there were no corrections to actual absentee ballots contained inside the envelopes as some have claimed. The witness signature and address information is all contained on the envelope in which the ballot is sent.
The Trump campaign is also alleging that voters got around Wisconsin's photo ID requirement by claiming they were indefinitely confined and therefore didn't have to present a photo ID in order to return their absentee ballot.
Wisconsin law requires all voters to show an acceptable photo ID to vote both in person and by mail. It does provide exceptions for citizens who are indefinitely confined because of age, physical illness or infirmity or are disabled for an indefinite period.
The Wisconsin Republican Party sued Democratic Dane County Clerk Scott McDonell over the advice he had posted on his Facebook page. The Wisconsin Supreme Court ordered McDonell to stop issuing guidance that is different from official language approved by the Wisconsin Elections Commission.
The Trump campaign also alleges that local election clerks issued absentee ballots to voters without requiring an application, in violation of state law. No evidence of wrongdoing related to absentee ballot applications has been made.
Republicans had raised concerns about events held over two weekends at Madison parks where poll workers accepted completed absentee ballots from people. But no ballots were handed out at that event, only those previously requested were accepted and there were no legal challenges filed.
Elections commission members Knudson and Thomsen both said they did not know what Trump was referring to in that complaint.
"This was news to me that that's been happening," said Knudson, a Republican.
Thomsen, a Democratic member, said the claim was "not true."
"Everyone knows you can't get an absentee ballot unless you request it," Thomsen said.
The goal is to start the recount in Dane County, at a Madison convention centre, on Saturday and livestream it, McDonell said. The recount will be done 16 hours a day and will likely take the entire 13 days allotted to complete. Milwaukee County officials planned an update on their plans for later today.
"We know the result will be the same as it was," McDonell said. "It's what we saw across the state four years ago and this election, from my perspective, ran very smoothly."
Recounts in Wisconsin and across the country have historically resulted in very few vote changes. A 2016 presidential recount in Wisconsin netted Trump an additional 131 votes.
Trump won Wisconsin by fewer than 23,000 votes that year and opposed the recount brought by Green Party candidate Jill Stein.
"The people have spoken and the election is over," Trump said at the time. "We must accept this result and then look to the future."
- AP