The Conservatives have again called for Home Secretary Charles Clarke to be sacked, saying "enough is enough" in the hunt for missing foreign criminals.
Asmar was arrested after a tip-off from a member of the public in Hull
Shadow Commons leader Theresa May asked if the arrest of a recommended deportee over a sex assault could be "sufficient reason" for Mr Clarke to be sacked.
Labour's Geoff Hoon rebuffed the call, accusing Mrs May of "blustering".
The Lib Dems say Mr Clarke's pledge to consider deportation for all foreign criminals would make little difference.
Arrest in Hull
Caliph Ali Asmar, an Iraqi Kurd aged 25, is being held in Hull in connection with an alleged sexual assault on a 15-year-old and the separate stabbing of a man in the city.
He was arrested after a member of the public saw appeals for information. Four other men were also detained for assisting an offender.
Mr Asmar arrived in the UK in 2001 but was refused asylum.
Ms May said this particular case "shows the dangers to which the public have been exposed by the incompetence of this government".
Asked whether Mr Asmar, also known as Shwana Ali Mohammed, had been recommended for deportation, a Home Office spokesman said he would not comment on individual cases.
More than half 79 most serious criminals have been freed, with 32 accounted for, deported or under Home Office control
Deportation has started to be considered in 574 of the 1,023 cases of prisoners involved in the controversy
Deportation is being pursued in 446 of the cases - the Home Office has not said how many of these prisoners are still at large
Police are continuing their search for about half of the 79 most dangerous offenders on a list of 1,023 freed men.
They were released from prison without being considered for deportation.
Only 32 had been traced by Wednesday.
The home secretary has promised the law will be toughened to introduce the principle that foreign nationals who commit a crime, should "expect to be deported".
However, the Liberal Democrats have said this pledge is too little, too late.
"This is not some kind of silver bullet," said party leader Sir Menzies Campbell. "This is not something that is going to make a huge difference to the power of the Home Secretary.
"The home secretary has a very wide power at the moment: he can send someone back home if he believes their presence is not conducive to the public good. How much wider can you get?"
Deportation proceedings have begun on 574 of the 1,023 released men.
Police and immigration officials have conducted a series of raids across Britain to detain the most serious offenders.
Dual nationality cases
Speaking during business questions in the Commons, Mr Hoon said the issue had only come to light because of "impressive improvements" in Home Office practice since 1999.
Mr Hoon also confirmed the deportation of criminals would apply to anyone in possession of dual nationality.
The government must ensure that "those who come here for a variety of purposes do so within the law", he said.
"If they do break the law and are not British citizens then we take appropriate action, which must include deportation."
The home secretary briefed his Cabinet colleagues on the issue of missing foreign criminals at their weekly meeting on Thursday.
The Prime Minister's official spokesman reaffirmed that it was "a problem that been there for decades which we are beginning to address".
He added that "what we do have to do is make sure the interests of the country are recognised in rebalancing the system".