Claims that Education Secretary Ruth Kelly is about to lose her job have been rejected by Downing Street.
Ms Kelly has come under fire over the decision to allow a registered sex offender to work as a PE teacher.
A review is under way over the case of Paul Reeve, who had been cautioned for accessing banned images of children.
But Tony Blair's spokesman said Ms Kelly would remain in her post, adding: "A number of reports suggesting her job was in jeopardy are simply wrong."
Ms Kelly has also been trying to steer through school reforms which have been criticised by some Labour MPs, including Deputy Prime Minister John Prescott.
BBC political editor Nick Robinson said this made her "vulnerable", as she was "under target" from senior backbenchers unhappy at the government's plans.
Ms Kelly told reporters she took "full responsibility" for decisions taken in the department on whether people were placed on England's List 99, which bans people from working with children.
She would not say how many sex offenders had been cleared to work with children but added initial investigations suggested there were "only a small number".
Ms Kelly promised an immediate review of all the cases since the sex offenders' register was set up.
"These are really serious issues for child protection and the government," she said.
"Child protection is our number one priority, we have got to get it right."
She said she was looking to take steps to make sure all sex offenders were barred for life from working with children.
Speaking earlier, she said that with immediate effect she would personally consider any cases where a ministerial decision was needed on whether to include people on the list.
It is thought a junior minister decided not to place Reeve - who was given a job at the Hewett School in Norwich - on List 99.
Reeve resigned after police intervened.
'Lapse of judgement'
Ms Kelly has faced fierce fire in the media in recent days.
Liberal Democrat education spokesman Ed Davey has accused her of a lapse of judgement.
Conservative shadow education secretary David Willetts has said it is extraordinary that other sex offenders have been handled in a similar way.
He is demanding to know whether Ms Kelly took the decision in the Reeve case herself and if not, who did.
But the prime minister's official spokesman said the education secretary had Mr Blair's full support.
Asked if she would remain in her post during the expected Cabinet reshuffle, he replied: "Yes."
The spokesman said former top civil servant Sir Michael Bichard was already reviewing the rules on sex offenders in the wake of the Soham murders.
But the Reeve case had "sharpened" the need for that review.
Among the issues being considered would be whether such decisions should be take by ministers or by experts in the field.
The spokesman said the government was not trying to duck "legitimate questions" over the system.
Changes are the Cabinet are already due as Mr Blair has yet to replace John Hutton as Chancellor of the Duchy of Lancaster.
Mr Hutton moved from the post in November to become work and pensions secretary after David Blunkett was forced to resign.