David Cameron is examining the possibility of withdrawing on a temporary basis from the European convention on human rights as the government seeks to deport the radical Islamist preacher Abu Qatada, Downing Street has confirmed.

As the home secretary, Theresa May, prepares to make a statement to MPs, the prime minister's spokesman said that the possibility of a temporary withdrawal was discussed by the prime minister and senior ministers on Tuesday.

Asked whether the prime minister would rule out withdrawing from the convention on a temporary basis, the spokesman said: "The prime minister met with the home secretary, the justice secretary and the attorney general yesterday to discuss the case. I am not going to get into specifics on the details of what the government is considering. We are going to explore every option."

The Conservatives have used the Abu Qatada case to raise the possibility of withdrawing from the convention. But they have no support from the Liberal Democrats, which means this would have to be delayed until 2015 at the earliest. The remarks by the No 10 spokesman suggest that a temporary withdrawal, as a response to the Abu Qatada case, is now under active consideration.

May is to detail renewed diplomatic attempts to secure fresh assurances from Jordan that Abu Qatada will not face a trial based on torture-obtained evidence if he is deported from Britain.

The disclosure of new moves will come in her Commons statement to be made in the face of accusations that her legal strategy to deport the key figure in al-Qaida-related terror activity in Britain lies in ruins 12 months after she promised MPs he would soon be on a plane back to Amman.

The renewed row broke after the Judicial Office confirmed that she had suffered a further setback with the court of appeal turning down her attempt to take the Abu Qatada case to the supreme court.

The home secretary is now expected to try the last remaining legal avenue open to her – a direct appeal to the highest court in the land – in her move to overturn last month's appeal court ruling that Abu Qatada could not be sent back to Jordan when there was a real risk he would face a trial based on evidence obtained by torture. A spokesman for the Judicial Office said on Tuesday that the court of appeal had confirmed it had refused permission for the home secretary to appeal to the supreme court. Appeals have to be based on a fresh point of law.

A Home Office spokesman reacted to the decision by saying: "We are disappointed with the court of appeal's decision but will now request permission to appeal directly from the supreme court.

"The government remains committed to deporting this dangerous man and we continue to work with the Jordanians to address the outstanding legal issues preventing deportation."

The home secretary confirmed last week that Abu Qatada, who is being held in Belmarsh prison for breaching bail conditions, could still face prosecution in Britain. "He was arrested for breaching his bail conditions, and obviously consideration is being given in looking at the material that was discovered to see whether that leads to prosecution," May told MPs.

She is rapidly running out of legal options and May is likely to be anxious to reassure MPs that progress is being made on the second, diplomatic, strand of her twin-track strategy. She is expected to give further details to the Commons of the attempts to secure even stronger assurances from the Jordanians that he will face a fair trial on bombing conspiracy charges should he be returned.

The security minister, James Brokenshire, went back to Jordan last month for a further meeting with the prime minister, Abdullah Ensour.

The shadow home secretary, Yvette Cooper, insisted that the appeal court decision meant that May's legal strategy had now completely failed 12 months after the home secretary had promised he would soon be on a plane.

"Theresa May failed to appeal against the European court decision last year. It is no good the home secretary blaming the court when she didn't appeal when she had the chance," said Cooper.

"Instead the home secretary went back to square one in the British courts, insisting with great fanfare that her legal strategy would work. But she also failed to get sufficient assurances from Jordan to convince the British courts. What is she going to do now?"

Her anger was echoed on the Tory backbenches. Dominic Raab said Abu Qatada had been running rings around the British criminal justice system. "This case shows we urgently need to overhaul the law on deportation, scrap the Human Rights Act and start standing up for British democracy rather than kowtowing to the European court in Strasbourg," he said.

The three appeal court judges, who unanimously dismissed May's last legal attempt to deport Abu Qatada in March, reminded her in their ruling that "torture is universally abhorred as an evil", and states cannot expel someone where there is a real risk that they will face a trial based on evidence obtained by torture.

The appeal court ruling by the master of the rolls, Lord Dyson, with Lord Justice Richards and Lord Justice Elias, threw out the home secretary's attempt to overturn a ruling last November by the special immigrations appeals commission (Siac) in London blocking Abu Qatada's return to Jordan to stand trial because "there was a real risk he would be subject to a flagrant denial of justice".

The appeal court judges said they recognised, however, that Abu Qatada was "regarded as a very dangerous person" and that the British government considered him to be a danger to national security, adding: "It is entirely understandable that there is a general feeling that his deportation to Jordan to face trial is long overdue."

But the judges said the fact that he was considered a dangerous terrorist was irrelevant to their decision.