The home secretary says he "regrets" that 1,023 foreign prisoners have been allowed to walk free when they were meant to be considered for deportation.
Mr Clarke says the process has fallen down
They include three murderers and nine rapists, Home Office figures show.
Charles Clarke said he could not say "hand on heart" that they would all be tracked down but said he did not think it was a "resigning matter".
The Lib Dems accused ministers of incompetence. The Tories are demanding Mr Clarke answer to Parliament.
Conservative shadow home secretary David Davis accused Mr Clarke of trying to "smuggle out" the news rather than face MPs' questions.
"At the end of the day it's not good enough to blame officials, frankly it is a issue which affects the safety of the British public," argued Mr Davis.
He did not think Mr Clarke should consider his position as the problems began before his time in the job.
Commons speaker Michael Martin said he would ask Mr Clarke to explain why he had not made a Commons statement on the debacle.
Home Office Minister Tony McNulty said he was "very, very shocked" by the news but he did not think Mr Clarke should resign.
He said he "did not think it was a case of heads will roll but we'll see".
Downing Street says Tony Blair has "full confidence" in both Mr Clarke and Mr McNulty.
"It is unreasonable to expect ministers to know what is going on in every nook and cranny in their department," said Mr Blair's official spokesman.
Mr Clarke said the 1,023 prisoners, who were released between February 1999 and March 2006, should have been considered for deportation or removal.
He said the failure was "deeply regrettable" and conceded that people would be angered by the oversight.
So far the Immigration and Nationality Directorate (IND) has located 107 of the total, leading to 20 deportations.
Among the offenders, five had been convicted of committing sex offences on children, seven had served time for other sex offences, 57 for violent offences and two for manslaughter.
There were also 41 burglars, 20 drug importers, 54 convicted of assault and 27 of indecent assault.
The Home Office said it did not have full details of offences committed by more than 100 of the criminals.
'No blame game'
Mr Clarke said: "It is clear that the increasing numbers of cases being referred for consideration [for deportation] led to the process falling down."
Mr Clarke said he was not going to start pointing the finger at who was to blame for the error.
"Both the Prison Service and the IND failed to carry out their responsibilities in the way they ought to have done," he said.
"They have both taken steps to lead me to be confident that it is now being done properly."
He added: "I do not intend to resign over this issue."
The courts had recommended that 160 of the criminals should be deported from Britain at the end of their sentences, it emerged.
Lin Homer, the IND's director general, said 14 of the 160 had been found. Five of those had been deported and nine considered inappropriate for removal.
Liberal Democrat leader Sir Menzies Campbell said it was "extraordinary" that so many people convicted of serious offences had "simply disappeared".
"All the government's tough talk on crime counts for nothing in the face of this incompetence," he said.
The situation only became apparent after the cross-party Commons Public Accounts Committee asked questions about released foreign prisoners during a hearing last October.
Former Home Secretary David Blunkett called the problems "astonishing".
"My view is that heads should roll," said Mr Blunkett.
"There are too many people in the system who simply don't care. I fully support Charles Clarke in getting to the bottom of this."
Harry Fletcher, assistant general secretary of the National Association of Probation Officers, said the chances of tracking down large numbers of released prisoners was "remote".
The Home Office was "facing crisis", said Mr Fletcher.