US presidential candidate Hillary Clinton cast herself as the steady leader at a "moment of reckoning" for America, contrasting her character with what she described as a dangerous and volatile Donald Trump.

In the biggest speech of her quarter century in politics, Clinton on Thursday accepted the Democratic presidential nomination for the November 8 election with a promise to make the United States a country that worked for everyone.

"We are clear-eyed about what our country is up against. But we are not afraid," she said.

She presented a sharply more upbeat view of the country than her rival Trump offered when Republicans nominated him last week, and even turned one of Republican hero Ronald Reagan's signature phrases against the New York real-estate developer.

"He's taken the Republican Party a long way, from 'Morning in America' to 'Midnight in America,'" Clinton said. "He wants to divide us – from the rest of the world, and from each other."

Clinton portrayed Trump as a threat to the country, saying "a man you can bait with a tweet is not a man we can trust with nuclear weapons."

Vying to be the first woman elected US president, Clinton called her nomination "a milestone".

"When any barrier falls in America, for anyone, it clears the way for everyone. That's why when there are no ceilings, the sky's the limit," the 68-year-old Clinton said.

A reintroduction

While her speech was not as electrifying as those given by President Barack Obama and some other prominent Democrats at the Philadelphia convention, Clinton was authoritative and self-assured in her pitch to the American public.

She acknowledged some people still do not know her well.

"I get it that some people just don't know what to make of me. So let me tell you. The family I'm from, well no one had their name on big buildings," Clinton said in a reference to Trump, whose name is plastered across his properties.

She said her family built a better life and a better future for their children, using whatever tools they had and "whatever God gave them".

The speech capped a four-day nominating convention that opened in discord after a leak of hacked Democratic National Committee emails showed party officials favoured Clinton over primary rival Bernie Sanders, a US senator from Vermont.

Even though DNC Chairwoman Debbie Wasserman Schultz, a Clinton ally, resigned on Sunday, angry Sanders supporters throughout the week disrupted the convention and undermined efforts by Clinton and Sanders to present a united front.

On Thursday, people familiar with the matter said the FBI is investigating a cyber attack against another Democratic Party group, which may be related to the earlier hack against the DNC.

The incident at the Democratic Congressional Campaign Committee and its potential ties to Russian hackers are likely to heighten accusations, so far unproven, that Moscow is trying to meddle in the US election to help Trump.

Sanders supporters on Thursday wore fluorescent green T-shirts that said "Enough is Enough". Their occasional chants of protest were drowned out by Clinton supporters chanting, "Hillary!"

Clinton acknowledged Sanders and his supporters.

"I want you to know, I've heard you," she said. "Your cause is our cause."

Appeal to Republicans

She appealed to voters beyond the party, praising Arizona Senator John McCain, a former Republican candidate for president, as a war hero, and the military service of the son of Trump's running mate, Indiana Governor Mike Pence.

"I will be a president for Democrats, Republicans and independents," she said.

Clinton said it would be her "primary mission" to create more opportunities and more good jobs with rising wages, and to confront stark choices in battling determined enemies and "threats and turbulence" around the world and at home.

"America is once again at a moment of reckoning. Powerful forces are threatening to pull us apart," said Clinton, a former secretary of state. "No wonder people are anxious and looking for reassurance – looking for steady leadership."

The evening sounded at times more like a traditional Republican convention than a Democratic one. During retired General John Allen's remarks, chants of "USA!" filled the hall and large flags were brought in to be waved. Speakers, some of whom included military and police officers, made frequent mentions of religion and patriotism.

"I certainly know that with her as our commander-in-chief, our foreign relations will not be reduced to a business transaction, I also know that our armed forces will not become an instrument of torture," said Allen.

Clinton embraced her reputation as a policy wonk, offering a litany of proposals for tuition-free college, infrastructure investment, immigration reform, gun control, affordable child care, paid family leave and more.

"A fantasy universe"

Trump, a 70-year-old reality TV show host who has never held political office, is running just ahead of Clinton in a RealClearPolitics average of recent national opinion polls. They both garner high "unpopularity" ratings.

In a statement after the speech, the Trump campaign said Clinton had described "a fantasy universe", not reality.

"Hillary Clinton's speech was an insulting collection of clichés and recycled rhetoric. She spent the evening talking down to the American people she's looked down on her whole life," said Stephen Miller, senior policy adviser.

At a rally in Cedar Rapids, Iowa, earlier in the day, Trump said he did not want to watch the speech. "I think we'll stay here all night because I don't really want to go home and watch that crap," he said.

Trump has portrayed the country as being under siege from illegal immigrants, crime and terrorism and as losing influence in the world. He has proposed a temporary ban on Muslims entering the country and a wall along the border with Mexico to keep illegal immigrants out.

Khizr Kahn, a Muslim whose son was one of 14 Muslims killed while serving in the military since the September 11, 2001, attacks, drew cheers when he pulled out a pocket copy of the US Constitution and said he wanted to show it to Trump.

"Hillary Clinton was right when she called my son the best of America. If it was up to Donald Trump he never would have been in America. Donald Trump consistently smears the character of Muslims," he said.