"Hillary Clinton will make an outstanding president and I am proud to stand with her here tonight," Sanders said as his supporters and Clinton's offered competing chants.
The angry uproar in Philadelphia was a setback to Democrats' hopes their convention would be a smoothly run show of party unity in contrast to the volatile campaign of Republican nominee Donald Trump.
It was also a bitter reminder of the bruising months-long primary battle between Sanders, 74, a U.S. senator from Vermont, and Clinton, 68, a former secretary of state, who this week will become the first woman nominated for president by a major U.S. political party.
Michelle Obama linked the historic nature of Clinton's campaign with her husband's own role as the first black U.S. president.
"I wake up every morning in a house that was built by slaves, and I watch my daughters, two beautiful and intelligent black young women, playing with their dogs on the White House lawn," Obama said.
"And because of Hillary Clinton, my daughters and all our sons and daughters now take for granted that a woman can be president of the United States."
The tumult began before the convention opened, as Sanders drew jeers from his own supporters when he urged his delegates to back the White House bid of his former rival, Clinton, and focus on defeating Trump in the Nov. 8 presidential election.
"We want Bernie!" they shouted in anger at both Clinton's victory in the race for the Democratic nomination and emails leaked on Friday suggesting the party leadership had tried to sabotage Sanders' insurgent campaign.
"Brothers and sisters, this is the real world that we live in," he said, adding: "Trump is a bully and a demagogue."
Members of the crowd screamed back: “So is Hillary.” "She stole the election!" someone else shouted.
In the convention's first hours, party officials struggled to carry out business as angry Sanders supporters roared their disapproval, drawing a deafening response from Clinton delegates.
'ACT LIKE DEMOCRATS'
"We're all Democrats and we need to act like it," U.S. Representative Marcia Fudge of Ohio, the convention's chairwoman, shouted over the uproar.
Sanders tried to head off the disruptions, sending an email to delegates as the convention opened urging them not to interrupt the proceedings.
"Our credibility as a movement will be damaged by booing, turning of backs, walking out or other similar displays. That's what the corporate media wants. That's what Donald Trump wants," Sanders said in the email.
Several speakers pleaded for peace between the Democratic factions. Comedian Sarah Silverman, a Sanders supporter, said she would support Clinton "with gusto" and admonished the Sanders fans.
"To the 'Bernie or Bust' people, you're being ridiculous," she said, drawing a roar from the crowd and another round of competing cheers between Clinton and Sanders supporters.
Paul Simon greets the audience while performing. REUTERS/Jim YOUNG
She and U.S. Senator Al Franken of Minnesota then introduced Paul Simon to sing his 1970 classic "Bridge Over Troubled Water."
Trump gloated at the Democrats' opening day disorder.
"Wow, the Republican Convention went so smoothly compared to the Dems total mess," he wrote on Twitter.
As the convention opened, the Democratic National Committee issued "a deep and sincere apology to Senator Sanders, his supporters, and the entire Democratic Party" for the email flap and said it would take action to ensure it never happens again.
Democratic National Committee Chairwoman Debbie Wasserman Schultz resigned effective at the end of the convention over the controversy. At a morning gathering of Florida delegates, Sanders supporters booed Wasserman Schultz, who they accuse of trying to sabotage the campaign of the democratic socialist.
The emails exacerbated the distrust of Clinton among some Sanders supporters who view her as a Washington insider who is only paying lip service to their goals of reining in Wall Street and eradicating income inequality.
But U.S. Senator Jeff Merkley of Oregon, the only senator to endorse Sanders during the primary, told the convention that supporters of the two former rivals had plenty in common.
"Whether you spent this year feeling the Bern or you spent this year ready for Hillary, all of us are ready for an America that rejects discrimination and embraces diversity, that celebrates voter empowerment not voter suppression, that creates opportunity for all of us, not just the lucky few," he said.
A TRUMP LEAD
While Sanders has endorsed Clinton, the former first lady faces a difficult task winning over his backers in the fight against Trump. The New York businessman pulled ahead in at least one opinion poll on Monday, after lagging Clinton in most national surveys for months.
A CNN/ORC opinion poll gave Trump a 48 percent to 45 percent lead over Clinton in a two-way presidential contest.
Trump was formally nominated for president at a chaotic Republican convention in Cleveland last week.
Ed Mullen, 49, a delegate from Illinois, said he supported Sanders but would vote for Clinton in November. He said the protesters at the convention had a right to stay.
"Democracy is messy, people have disputes with how the DNC has managed this campaign," Mullen said.
The cache of leaked emails disclosed that DNC officials explored ways to undercut Sanders' insurgent presidential campaign, including raising questions about whether Sanders, who is Jewish, was an atheist.
The Clinton camp questioned whether Russians may have had a hand in the hack attack on the party's emails in an effort to help Trump, who has exchanged words of praise with Russian President Vladimir Putin. Republicans dismissed the suggestion as absurd.
The FBI said on Monday it would investigate the nature and scope of the hack.
(Additional reporting by Jonathan Allen, Amy Tennery, Alana Wise, Emily Stephenson and Erik Tavcar Writing by John Whitesides and Alistair Bell; Editing by Frances Kerry and Peter Cooney)