Home Secretary John Reid has been accused of "not telling the whole truth" about the terror suspect scandal.
It also emerged that police and prosecutors may not be able to take action against one of the missing men because officers had not handed him a new version of the control order before he disappeared.
Mr Reid insisted he was legally bound not to reveal the identities of the two men, known only as LL and AD.
But Shadow home secretary David Davis said: "The fact is he has not told the whole truth. He could have reported the fact that there had been two escapes without revealing the identities.
"The Home Secretary is deliberately avoiding the question as to why he did not inform Parliament about these escapes. He has blamed everyone else but himself for this fiasco."
Mr Davis added that there had been no moves by the Government or the police to lift the anonymity orders to inform the public of the men's identities.
LL, an Iraqi, vanished before the Court of Appeal quashed the earlier version of his control order and before police could issue him with a replacement. It could mean that technically he has committed no offence.
A Home Office spokeswoman said: "The police and CPS cannot prosecute LL for breach because the original control order in question was subsequently quashed by the Court of Appeal. It is open to the police and CPS to prosecute AD for breach of his control order once apprehended."
The British terror suspect, AD, was reportedly questioned about alleged links with the July 7 bombers. The 25-year-old was held in Pakistan late last year for more than six months. Pakistani authorities are reported to have questioned him about an alleged meeting in Pakistan with Aldgate bomber Shehzad Tanweer.
AD is also alleged to have been a friend of British suicide bomber Asif Hanif, who blew himself up in Israel in 2003. The allegations against him were reported in the New York Times in July last year, but Pakistani officials rejected the claims.
