Home Secretary Theresa May has disagreed with Labour over the effectiveness of the government's anti-terrorism control measures after a terror suspect absconded while under a TPim.
Ibrahim Magag disappeared from Camden, north London on Boxing Day; police were alerted when he "failed to meet his overnight residence condition" that night.
Mr Magag was previously subject to a control order but they were replaced by TPim control measures last January. The Home Office said his disappearance had nothing to do with the switch.
During Home Office questions on 7 January 2013, Labour's Yvette Cooper claimed TPims were "not sufficient" and called for a change in the law.
The shadow home secretary said there were no absconds in the last four years of the control order regime "when relocations were extensively used".
Mrs May had personally ruled out relocation for Mr Magag "and for every other terror suspect", even though the judge reviewing Mr Magag's control order said it was "too dangerous to permit him to be in London even for a short period", she claimed.
Ms Cooper called for a review into Mr Magag's disappearance, and for the home secretary to admit "she got it wrong on relocations".
Mrs May queried the shadow home secretary's use of statistics, pointing out there had been "seven absconds" in the whole six year period of control orders.
"She cannot argue that control orders were stopping people from absconding and TPims are not," the home secretary said.
Mrs May told the Commons the police were doing "everything in their power" to find Mr Magag "as quickly as possible".
TPims restrict the movements of people thought to pose a risk to the public, but who cannot be tried for reasons of national security.