Gordon Brown will look "weird" and out of touch if he presses on with ID card plans despite the loss of child benefit records, David Cameron has said.
Mr Cameron said the PM should "stop and think" about policy
At prime minister's questions, the Tory leader said the data problems should cause Mr Brown to "stop and think".
But the prime minister told MPs that using biometric profiles would ensure "people can feel confident that their identity is protected".
All UK passport applicants are due to be issued with ID cards from 2010.
The government says ID cards will help protect people from identity fraud, tackle illegal immigration, stop people who are not eligible from using public services and disrupt criminals and terrorist activities.
But the Tories and Lib Dems say they threaten individual liberties, will be open to fraud and will cost too much.
Fresh questions about the scheme have been asked after the revelation that two computer discs containing millions of people's names, addresses and bank details had been lost by HM Revenue and Customs.
Mr Cameron said: "If the prime minister really wants to learn some lessons from this, will he recognise this appalling blunder comes at a time when the government is planning a national identity register, to bring together private and personal details of every single person in this country?
"Will the events of the last few days cause the prime minister to stop and think about this policy?
People were "desperately worried", he said, adding: "They will find it truly bizarre.
"They'll find it weird that, frankly, the prime minister doesn't want to stop and think about the dangers of a national identity register.
"Won't people think that he's completely lost touch with reality, he's demonstrating no common sense at all?
"Won't they see a prime minister who tries to control everything but actually can't run anything?"
Mr Brown replied that 22 out of 25 European countries had ID cards.
He added that Mr Cameron's "own security adviser proposes identity cards. His own reviewer of the national police force - the border force - says he's in favour of identity cards".
"What we've got to ensure is that identity fraud is avoided and the way to avoid identity fraud is to say that - where people have passport information - then we will have the biometric support that is necessary so that people can feel confident that their identity is protected."
But Labour MP Karen Buck, a member of the Commons home affairs committee, called for a "pause" on progress with ID cards.
She told BBC Radio 4's The World at One: "The worst thing in the world would be to plough on and say 'We're going ahead with this' until we have had a chance for proper reflection and measure where public opinion stands when this has calmed down."
Fellow Labour MP Andy Love, who sits on the Treasury committee: "It is sensible in the circumstances to stand back for a while."
On Tuesday, acting Lib Dem leader Vince Cable said: "After this disaster how can the public possibly have confidence in the vast centralised databases needed for the compulsory ID card scheme?
"Where does the buck stop after this catalogue of disasters?"
The national co-ordinator of the NO2ID campaign against identity cards, Phil Booth, said: "This data disaster shows up the madness behind the government's ID schemes.
"It's bad enough that HMRC can't be trusted with basic financial details. But within five years the Home Office could be leaking or losing people's complete identity records."
Biometric cards will be brought in for foreign nationals from next year.
The projected cost of the identity card scheme will be £5.612bn over the next 10 years, the Home Office said earlier this month.