Michelle and Barack Obama gave resounding endorsements of Kamala Harris on Tuesday night at the Democratic National Convention, exhorting party supporters across the US to turn out and vote to defeat Donald Trump in November.

"Hope is making a comeback," Mrs Obama told the crowd at the DNC in Chicago, echoing her husband's campaign promise of "hope and change".

In their back-to-back speeches, the Democratic Party's most popular figures praised Ms Harris, while excoriating Trump - whose presidency was characterised by "bluster and chaos", in the words of Mr Obama.

But the couple also warned their party not to lose sight of what remains an extremely tight race amid the enthusiasm for Ms Harris's campaign. They stressed the election would be decided in a handful of key swing states.

"Make no mistake, it will be a fight,” said the 63-year-old former president Mr Obama.

Michelle Obama, 60, stressed the point further. "We need to vote in numbers that erase any doubt," she said. "We need to overwhelm any effort to suppress us."

Mr Obama emphasised America's preparedness for a "new chapter", adding: "We are ready for a President Kamala Harris. And Kamala Harris is ready for the job."

The Obamas' appeal to Democrats to turn out in November exposed a deeper party anxiety about the narrow race between Ms Harris and Trump, who retains a tight hold on his loyal base of supporters across the country.

Ms Harris has a narrow lead in national polling averages but pollsters caution that the race remains a virtual tie in the handful of battleground states that will ultimately decide who wins under America's electoral college system.

Though Ms Harris is technically the incumbent candidate, she has described herself and her running mate, Minnesota Governor Tim Walz, as the underdogs in the race.

The Obamas also acknowledged the renewed sense of excitement within the party since Ms Harris replaced President Joe Biden following his exit from the race - making a tacit reference to the enthusiasm and message of hope that powered Mr Obama to victory in his 2008 presidential run against Republican John McCain.

Mr Obama also went on to serve a second term, before Trump won the White House in 2016.

Mrs Obama, whose most memorable line from her last convention speech in 2016 was, "when they go low, we go high", did little to lower the temperature of the heated political rhetoric that has divided the country over the last decade.

She attacked Trump for assailing her family and continuing to push "ugly, misogynistic, racist lies as a substitute for real ideas and solutions that will actually make people's lives better".

In a broadside that generated some of the loudest cheers of the night, she mocked Trump for his use of the term "black jobs" on the campaign trail.

"Who’s going to tell him that the job he’s currently seeking might just be one of those black jobs?" she said, referring to her husband's presidency.

Mrs Obama also used her platform to remember her late mother, Chicago-raised Marian Robinson, who died earlier this year aged 86.

"I wasn't even sure if I could be steady enough to stand before you tonight, but my heart compelled me to," she told the audience.

Trump and running mate JD Vance have been holding rallies and events in swing states while the Democrats gather in Chicago.

On Tuesday afternoon, Mr Vance used a news conference in neighbouring Wisconsin to attack Ms Harris over the "failures" of her vice-presidency.

He zeroed in on crime and public safety, and the economy - two areas where the Republicans see a vulnerability.

Referring to protests in the city of Kenosha after the police shooting of black man Jacob Blake in 2020, he said: "Wisconsin has suffered when you don't have good, smart, pro-public safety and leadership, and that’s what Donald Trump and I want to bring back to the White House.”

Having travelled to Wisconsin, Ms Harris was not present at day two of the convention in Chicago. But the event did feature a jubilant and star-studded roll call, with delegates from each state - as well as US territories - symbolically casting a vote for Ms Harris and Minnesota Governor Tim Walz in the arena.

Though the vice-president formally clinched her party’s nomination earlier this month, the symbolic gesture quickly turned into a dance party.

Lil Jon performed Turn Down For What before Georgia’s announced its vote. Actor Sean Astin spoke during Indiana’s turn, a nod to his role in the cult classic American football film Rudy, which is set in the state.

An on-stage DJ spun songs for each state as delegates, on their feet and wearing bracelets that flashed red and white, delivered short speeches about why they were supporting Ms Harris and Mr Walz.

The vice-president then virtually addressed the crowd from her rally in Milwaukee - 90 miles away - at the same venue where Trump accepted his party's nomination four weeks ago.

"We are so honoured to be your nominees," she said of herself and Mr Walz. "I'll see you in two days, Chicago."

Before the Obamas gave their speeches, Second Gentleman Doug Emhoff, Ms Harris's husband, made his own appearance to share personal stories about the vice-president - including how they were set up on a blind date by one of his clients in 2013.

He spoke about their "big, beautiful, blended family", referring to his son, Cole, and daughter, Ella, from his first marriage. He described Ms Harris as a "joyful warrior" and a supportive parent who put their family first despite the demands of her job.

Ms Harris, who was flying back from her rally during her husband's speech, kept Air Force Two in the air so she could watch his speech live, the White House said.

Mr Emhoff said the two would celebrate their 10th anniversary on Thursday night, when Ms Harris formally accepts the party's nomination in a primetime speech.

"Kamala was exactly the right person for me at an important moment in my life," he said. "And at this moment in our nation's history, she is exactly the right president."