The terror suspect who escaped surveillance by disguising himself as a woman in a burqa was under restrictions to stop him travelling overseas to support terrorism, the home secretary has told MPs.

Theresa May defended the use of terrorism prevention and investigation measures, or Tpims, after the disappearance of the Somali-born suspect, Mohammed Ahmed Mohamed, from a west London mosque on Friday.

Mohamed, 27, is a British citizen and is the second suspect on a Tpim order to go missing in the last year. The first, Ibrahim Magag, disappeared off the security service's radar after he ripped off his tracking tag and jumped into a black cab in Camden Town, north London.

Mohamed went missing from the mosque in Acton, west London, only hours after an Old Bailey prosecution against him for tampering with his electronic tag was discontinued when the crown offered no evidence.

May said the police and security services did not believe Mohamed represented a direct threat to the British public. But he has been linked with the Somali militant group al-Shabab, and is believed to have helped various individuals to travel from Britain to Somalia to engage in terrorism-related activity.

The Metropolitan police counter-terrorism command has launched an intensive hunt. His photograph and details have been circulated to all ports and airports. May said the police held his UK passport.

She defended the Tpims regime, saying its abscondence record was little different to that of the control-order regime, which it replaced last year, under which seven terror suspects disappeared in six years.

"The police and security service have confirmed that they do not believe that this man poses a direct threat to the public in the UK," she said. "The reason he was put on a Tpim in the first place was to prevent his travel to support terrorism overseas." In the Commons, May also repeatedly had to reject calls from backbench Tories to ban the burqa and other face coverings after Mohamed's disappearance: "It is not for the government to tell women how to dress," she told them.

The shadow home secretary, Yvette Cooper, claimed the replacement of control orders with Tpims last year had made it easier for terror suspects to abscond. So far, two out of the 10 suspects placed on Tpims have gone missing.

Cooper particularly blamed the scrapping of "internal exile"or relocation orders, which would have left Mohamed unable to return to London to keep in contact with his network. Court documents show that the first suspect to abscond, Magag, was also a member of the same UK-based network supporting terrorism-related activity in Somalia.

"She was warned about changing the law, she was warned about weakening controls, she was warned more people would abscond and they have – twice -but still she won't act. The question on everyone's lips is how many more warnings does this home secretary need?," said Cooper.

But May insisted that lessons had been learned since the first Tpims subject had disappeared. She said that resources for surveillance had been increased in the wake of the move from control orders to Tpims. The home secretary said it wrong to claim that control orders could prevent absconds – 7 had disappeared in the six years they had been in force.

Perhaps most surprisingly, the home secretary, faced demands from three Tory MPs to introduce a ban on face coverings, including the burka, as a result of the case. One, Sir Gerald Howarth, said the burka should be banned "because it is alien to our culture, and has enabled this man to abscond". It was a demand May found easy to dismiss saying while there were times, such as at the border or in court, when it was right to require face coverings to be removed, but as a matter of principle "it is for an individual woman to decide how she dresses herself".

The Tpims regime allow the home secretary to impose restrictions on travel, communication, finance and an overnight curfew of terror suspects who cannot be prosecuted or deported. Tpims can be extended for a year for another 12 months before they expire.