Health Secretary Patricia Hewitt should lose her job after security concerns were raised about a junior doctor job application website, the Tories say.
Doctors have protested about the application system
The Medical Training Application Service (MTAS) site was suspended last week after two separate lapses.
Shadow health secretary Andrew Lansley said junior doctors wanted to see her go and the next prime minister should move her from her post.
Ms Hewitt told the Commons the security breaches were "utterly deplorable".
The Department of Health has already launched an investigation into the security concerns.
It has been claimed doctors were able to read each other's messages and that applicants' personal information could be freely accessed.
Ms Hewitt said that there was no evidence that members of the public or other unauthorised people had accessed personal information on the website.
But she told the Commons that she apologised to junior doctors.
She said the MTAS website had been suspended and would remain so until the Department of Health was confident it was secure.
"There is no doubt that confidence in the application system MTAS has been further damaged by these appalling security breaches," she added.
Mr Lansley said the security breaches had been "astonishing and outrageous".
He said the information included highly sensitive data such as sexual orientation and criminal records.
He added the medical profession had lost confidence in her and junior doctors wanted her to resign.
"She is not going to go but the next prime minister ought to move her. I hope he does."
Lib Dem health spokesman Norman Lamb said: "This could and should have been avoided if there had been adequate piloting."
Emily Rigby, Chair of the British Medical Association's Medical Students Committee, said her members were not confident that applicants' personal information had not been accessed from the website.
She said Ms Hewitt could not say for certain that no criminal offences had been committed.
"It is totally unacceptable that students are left wondering if their identities could have been stolen," she said.
"Many students are studying for their finals at the moment; this is an added stress they should never have had to deal with.
"We need an absolute assurance from the Secretary of State that no students were affected and a promise that it can never happen again."
The security lapses are just the latest in a series of problems that have dogged the revamp of the junior doctor training system.
MTAS has also been criticised for being badly designed and junior doctors have objected to the fact that there are estimated to be 10,000 more applicants than posts under the Modernising Medical Careers scheme.
Junior doctors have already called for Health Secretary Patricia Hewitt to resign over "shambolic" medical training reform.
Thousands of trainee medics marched through London in March in protest after many well qualified candidates were left without a single interview.
And an independent review has been launched to see what changes are needed to the system for next year.