But he was backed by senior Conservative Sir Malcolm Rifkind, who told MPs that, while he had not voted for him last year, he had been "impressed" by his 11 months in the job and hailed Mr Bercow as a "modern Speaker for a modern age".
When opponents failed to force a vote, he was dragged to the Speaker's chair by his supporters, in keeping with parliamentary tradition.
There was some laughter as Mr Bercow called the prime minister to speak and there was a brief pause - with MPs telling Mr Cameron: "That's you."
The new PM said he was glad to see Mr Bercow had been re-elected to his seat by Conservative voters - despite a high-profile challenge by UKIP's Nigel Farage.
The Commons benches were packed for the short session, the first since the election, with some MPs unable to get a seat.
We will be a strong, effective, self-confident and determined opposition, holding this government to account
In his opening speech, Mr Cameron said there were lots of new MPs, including more women and more black and Asian MPs. With Lib Dem leader Mr Clegg beside him, he joked: "It really does look and feel different - indeed many of us are sitting next to people that we have never sat next to before."
Mr Cameron added: "This is a new era for our politics and something of a new start, the chance for a new generation to show just how good this place can be."
He added that the "real tests" of the new Parliament were to build trust between Parliament and the people and making the "right decisions".
"It's within our gift to do this and it's our responsibility to make sure we do," he said.
Ms Harman and her Labour colleagues are on the opposition benches for the first time since 1997.
She advised new MPs to ignore advice to keep their heads down for the "first 10 years" and instead "blaze a trail".
She told the new prime minister: "Can I offer my congratulations to you. You have an awesome and a heavy responsibility.
"We all agree that we need strong and stable government. But we also should agree that we need strong opposition."
New MPs, after all the slog of campaigning, may feel like king or queen of their constituency. But it's time to get used to their place - the bottom - of the parliamentary pecking order.
To cheers from her colleagues, she added: "We will be a strong, effective, self-confident and determined opposition, holding this government to account."
There was no speech from Mr Clegg as Lib Dem leader, now he is part of the government.
Instead SNP Westminster leader Angus Robertson said it would be for the parties of Scotland, Wales and Northern Ireland to take on more of the work of scrutinising the government.
Separately, Labour MP Jim Sheridan also raised a point of order about the government's plans for fixed-term parliaments, which would include allowing MPs to dissolve Parliament - but only if 55% vote to do so - something he described as "the Mugabe question".
And Labour former Cabinet minister David Blunkett expressed concerns that the new government had made announcements outside the Commons on changing the voting system, Lords reform, spending cuts and the mechanism for dissolving Parliament.
Some 227 new MPs were elected on 6 May, resulting in a hung parliament and a subsequent Conservative-Lib Dem coalition.
The swearing-in of MPs is expected to last into Thursday, with the most senior going first. MPs can take a religious oath or a secular affirmation of loyalty to the Crown.
The serious business of the Parliament gets under way next week, with the Queen's Speech - outlining the coalition's legislative agenda for the year - taking place on Tuesday.
Party breakdown: See how the Commons has changed, 2005-2010
There are 227 new MPs this Parliament, out of 649 MPsFigures exclude "retreads" - five MPs who have been in a previous Parliament but not directly preceding 2010
There are 142 women MPs this Parliament, out 649 MPs
Of the 649 MPs this Parliament, 26 are black and minority ethnic
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