Home Secretary Charles Clarke is set to update MPs on Wednesday about efforts to track down foreign prisoners who were released and not deported.
Conservatives sparked the calls for Mr Clarke's statement
The Tories had requested an "urgent" statement to MPs. Later this month Mr Clarke will also appear before the home affairs select committee on the issue.
Tony Blair meanwhile has sought to repair damage done to Labour's local election prospects by recent scandals.
Mr Blair has been forced to defend Mr Clarke and his deputy John Prescott.
During his campaign tour of the north-west of England on Tuesday he urged supporters to think about the government's achievements - and not the last few days' headlines.
Both the home secretary and Mr Prescott, who has admitted having an affair with his diary secretary, are resisting pressure to resign.
Mr Prescott was meeting the prime minister on Tuesday afternoon but Downing Street says the talks are only "routine".
With the two ministers' actions crowding out any positive message Labour had hoped to get across before Thursday's local elections in England, Mr Blair is trying to steer the campaign back on course.
On the ninth anniversary of becoming prime minister, he acknowledged that the government had been going through a difficult period but urged people to look at the "bigger picture" before they voted on Thursday.
Speaking to the retail workers' union Usdaw in Blackpool, Mr Blair said people should remember the party's achievements on the economy, schools, hospitals, for pensioners and children and in anti-social laws.
The Commons home affairs committee meanwhile has announced that it will investigate the debacle of the released prisoners.
The MPs will question both Mr Clarke and Home Office officials.
Press Association also reported that it had seen a 90-page circular setting out a strict timetable for considering foreign prisoner deportations sent on 31 March 2005 - meaning the Home Office was releasing prisoners for a year while those rules were in force.
The document, Prison Service Order 6000, describes a fail-safe system to deal with cases of foreign prisoners that had slipped through the net, with prisons told to identify whether inmates were liable to deportation as soon as they arrived at the jail.
Conservative leader David Cameron urged Mr Blair to carry out a Cabinet reshuffle and "say goodbye" to Mr Clarke.
And, following a weekend of further revelations about Mr Prescott's affair with his secretary, Mr Cameron said that while that was "a private matter, clearly he looks a fool".
Mr Cameron instead focused on Mr Prescott's "woeful record" as a minister on issues such as regional government and housing.
Liberal Democrat leader Sir Menzies Campbell said Labour was clearly "on the ropes" and was "failing nationally and locally".
"It is now inevitable that many voters will use Thursday's poll as a referendum on the prime minister," he said.