Democrat Joe Biden held a narrow lead over President Donald Trump in Wisconsin after officials completed their vote count and pulled further ahead in Michigan, even as the Republican incumbent’s campaign vowed to pursue a recount and a lawsuit to challenge the results in the two Midwestern battleground states.

CNN and AP project Joe Biden to win Wisconsin's 11 electoral votes, which would widen his path to victory if counts hold in Michigan. But Wisconsin's votes will likely be recounted and the Trump campaign is suing to halt vote counts in Michigan.

Democratic presidential nominee Joe Biden acknowledged the historic nature of the election and how more than "150 million people cast their votes" this year during a speech in Wilmington, Delaware.

"More Americans voted this election than ever before in American history. Over 150 million people cast their votes. I think that is just extraordinary. And if we had any doubts, we shouldn't have any longer about a government of, by and for the people. It is very much alive, very much alive in America," Biden said.

Biden added: "Now after a long night of counting, it's clear that we are winning enough states to reach 270 electoral votes needed to win the presidency. I'm not here to declare that we have won, but I am here to report when the count is finished, we believe we will be the winners."

As Joe Biden gets closer to the 270 electoral votes to win the presidential election, he talked about how he would be a leader for everyone – not just the people who voted for him – in an address calling for unity and bipartisanship on Wednesday.

"We are campaigning as Democrats, but I will govern as an American president," Biden said. "The presidency, itself, is not a partisan institution. It's the one office in this nation that represents everyone and it demands a duty of care for all Americans and that is precisely what I will do."

He talked about the anxiety and division that many Americans feel, saying that although there are opposing views across the country "we have to stop treating our opponents as enemies."

"We are not enemies. What brings us together as Americans is so much stronger than anything they can tear us apart," Biden said.

"It's time for us to do what we have always done as Americans – to put the harsh rhetoric of the campaign behind us, to lower the temperature, to see each other again, to listen to one another, to hear each other again and respect and care for one another. To unite, to heal, to come together as a nation," he added.