Donald Trump and Kamala Harris delivered their closing arguments, holding duelling rallies across the battleground states well into the night, on the last day of campaigning before the US election.

Harris was in Pennsylvania, the biggest swing state and crucial to the Democratic campaign. She held the final rally of her campaign at the steps of the Philadelphia Museum of Art, made famous in the movie Rocky. Introduced by Oprah Winfrey and Lady Gaga, Harris emphasised her message of hope. “We finish, as we started, with optimism, with energy, with joy,” she said. “We need to get to work.”

Trump struck a darker tone in the same state, with threats to put tariffs on all imports from Mexico unless it stopped migrants from entering the US – though he interrupted himself at one point to celebrate his endorsement from podcaster Joe Rogan. The Republican candidate also held hours-long events in North Carolina and Michigan.

Leading forecaster Nate Silver has released his final forecast, and said that Harris won in 40,012 out of 80,000, or 50.015% of, simulations run using his model. Polls released on Monday found Harris had a marginal lead in Michigan but was tied with Trump in Pennsylvania and other key swing states. Trump has held on to a lead in betting markets but one that is eroding.

Here’s what else happened on the last day of the 2024 election campaign:

Donald Trump election news and updates

• Trump held his final rally of the campaign in Grand Rapids, Michigan – the same place where he closed his 2016 and 2020 campaigns. “With your vote tomorrow, we can fix every single problem our country faces and lead America – indeed, the world – to new heights of glory,” he told the crowd.

• The former president started the last day of campaigning in North Carolina, launching personal attacks on a number of high-profile Democratic women, then travelled to Reading, Pennsylvania, where he painted migrants as dangerous criminals. “November 5, 2024 will be Liberation Day in America,” he said. “And on day one, I will launch the largest deportation program of criminals in American history.”

• In Pittsburgh, Pennsylvania, Trump praised the Green party presidential candidate, Jill Stein, as “one of my favourite politicians” and relished the prospect of a return to the White House: “Only one day – does that sound nice – one day from now. We’ve been waiting four years for this.”

• JD Vance, Trump’s running mate, was once again condemned for misogyny after repeatedly calling Kamala Harris “trash” at campaign rallies. The Republican vice-presidential nominee compared Harris to trash at a New Hampshire rally on Sunday, then did it again on Monday in Flint, Michigan, and Atlanta, Georgia.

Kamala Harris election news and updates

• The vice-president started the day in Scranton, Joe Biden’s childhood home town, where she told supporters to “get this done”. Biden did not appear with Harris in Scranton, continuing her campaign’s effort to put a gap between the candidate and her former running mate.

• Harris reached out to the Puerto Rican and Latino population of Pennsylvania, visiting a Puerto Rican restaurant in Reading with congresswoman
  Alexandria Ocasio-Cortez and governor Josh Shapiro and appearing at an Allentown rally with rapper Fat Joe, who ripped Trump for his treatment of Puerto Ricans and Latino voters: “[If] you’re not decided, where’s your pride as a Latino?”

• Harris went doorknocking in Reading and held a rally in Pittsburgh, supported by pop star Katy Perry. The vice-president sought to strike a positive tone, saying it was time to move past the “fear and division” of the past decade and, drawing a contrast with Donald Trump without mentioning his name. “It is time for a new generation of leadership,” she said.

• Harris headed home to Number One Observatory Circle in Washington in the wee hours of Tuesday morning after her final Philadelphia rally. She will spend Tuesday calling into local radio stations in the seven battleground states to reach the remaining voters, her communications director told reporters.

• Harris’s running mate, Minnesota governor Tim Walz, campaigned across his home state before visiting Wisconsin, where he struck a hopeful tone: “Look at the movement, and look at the energy that Kamala Harris has built in 107 days – imagine what she can do for the next eight years.” Walz ended Monday in Michigan, appearing with Jon Bon Jovi, and told supporters women will send a message to Trump tomorrow “whether he likes it or not”.

Elsewhere on the campaign trail

• A Pennsylvania judge rejected legal challenges to Elon Musk’s $1m giveaway, allowing the billionaire’s voter sweepstakes to continue through Tuesday’s presidential election.

• Republicans also had a win in their legal battle over vote eligibility, after Georgia’s highest court ruled absentee ballots must be returned by election day. As legal challenges play out across the country, the Harris campaign told reporters it was prepared to combat any efforts by Trump to discredit the outcome.

• The Harris campaign expects “near complete results” on election night from Georgia, North Carolina and Michigan, along with partial results from Pennsylvania, Wisconsin and Arizona, according to campaign chair Jen O’Malley Dillon.

• Officials have begun preparing for a feared escalation of political violence on election day and beyond. More than two dozen states are willing to send national guard troops to Washington, national guard officials said, while election officials in one Nevada county said polling places have installed “panic buttons” in the wake of surging threats. A group of Democratic secretaries of state have asked social media companies how they will moderate inflammatory content as violent threats and disinformation spread.

Read more of the Guardian’s 2024 US election coverage: