The government has "important questions to answer" over anti-terror laws after a suspected terrorist went missing, Theresa May said.
Ibrahim Magag, 28, absconded from a Terrorism Prevention and Investigation Measures (Tpims) notice after failing to meet his overnight residence condition on Boxing Day.
Ibrahim Magag from Somalia
He had previously been subject to a control order and was relocated to the West Country. Under new Tpim laws, forced relocation is no longer possible.
Shadow home secretary Yvette Cooper said the case raised "important questions".
"The priority right now must be to find Ibrahim Magag, and I agree with the Home Secretary's decision to remove the suspect's anonymity," she said.
"But the Home Secretary and the police also need to answer important questions about how Ibrahim Magag has been able to abscond.
"Ibrahim Magag was previously on a control order and relocated to the West Country - a decision upheld by the courts.
"The Home Secretary took the decision against the advice of security experts to replace control orders with Tpims, removing the power to relocate terror suspects and reducing restrictions. She also assured Parliament that surveillance would be sufficient to fill the gap.
"Theresa May needs to explain rapidly why surveillance failed on Ibrahim Magag since Christmas and whether her decision to return him to London and to weaken legislation has made it easier for him to abscond and harder for the police to find him."
Theresa May has been criticised
The government has denied that his disappearance has anything to do with the replacement of control orders with Tpims. however Labour MP Pat McFadden accused the government of "watering down" the previous control orders regime.
"To take these suspects and give them access to mobile phones and the internet, the government chose to disarm itself from the powers to relocate suspects and I believe this gentleman was previously excluded from coming to London.
"He has used his new-found, government-given freedom to come back to London and has now absconded. What they have done is put the public at greater risk by watering down our anti-terror laws and putting needless extra pressure on the security services," he told BBC Radio 4's The World at One.
"I think what they have done is complacent and dangerous and I warned the Home Secretary and the Prime Minister about this when the legislation was going through,"
David Anderson QC, the independent reviewer of terrorism legislation, told the programme the replacement measures were "still pretty oppressive".
The end of relocation powers had been balanced by increased resources for surveillance, he said, and Tpims were limited to two years as opposed to the indefinite length of control orders.
Police continue to search for Magag.
A Metropolitan Police spokesman said last night: "The Counter Terrorism Command immediately launched inquiries to trace the man and these continue. Public safety remains our priority.
"At the request of the police an anonymity order imposed by a court was lifted today to allow a public appeal.
"Anyone who sees this man or knows of his whereabouts should not approach him, but call 999 immediately."
He added: "Ibrahim Magag is not considered at this time to represent a direct threat to the British public."
Magag is described as a black man of Somali origin, 6ft 2in and slim to medium build. He has a beard, but detectives warned he may try to change his appearance.
He was last seen wearing a khaki robe, a black Berghaus windcheater and navy Converse trainers.
Security Minister James Brokenshire said: "National security is the government's top priority and the police are doing everything in their power to apprehend this man as quickly as possible.
"The Home Secretary, on police operational advice, applied to the High Court for an order protecting anonymity to be lifted in order to assist with their investigation.
"The Terrorism Prevention and Investigation Measure in this case was intended to prevent fundraising and overseas travel. We do not believe his disappearance is linked to any terrorism planning in the UK."
Anyone with information is asked to contact the confidential Anti-Terrorist Hotline on 0800 789 321.