The home secretary, Theresa May, has been forced to admit that the radical Islamist cleric Abu Qatada will remain in Britain for many months yet, despite announcing she had signed a new treaty with Jordan designed to finally clear the way for his deportation.

Her stance led some rightwing MPs to accuse her of having surrendered, as she distanced herself from suggestions earlier on Wednesday that the UK could temporarily withdraw from the European convention on human rights. In the end May simply described that policy as an option.

The Liberal Democrats insisted there was no official plan to withdraw from the ECHR, while the former lord chancellor Kenneth Clarke, the minister without portfolio who attends cabinet, said: "It's not the policy of this government to withdraw either from a short period or for a lengthy period from the European convention on human rights."

Number 10 said on Tuesday that David Cameron's blood was boiling over the Abu Qatada case, but seemed to accept that May will be unable to push ahead with any temporary withdrawal from the ECHR, partly due to coalition divisions. Downing Street said that if the British courts continued to refuse to deport Abu Qatada, Cameron would ask Nick Clegg what he intended to do.

In her statement to MPs, May said the new Jordan agreement would include new guarantees that Abu Qatada would get a fair trial, which would overcome the objections from the British courts that he would face "a flagrant denial of justice" if he were sent back to face terror charges based on evidence obtained by torture.

The new "mutual legal assistance agreement" is expected to be ratified by parliament by the end of June. The home secretary said that while it would not mean that Abu Qatada would "be on a plane within days", it would give the government "every chance in succeeding" in sending him back to Jordan.

May also confirmed under questioning by MPs that the government was "exploring all options" in the case, including possible temporary withdrawal from the European convention of human rights. "We should have all the options, including leaving altogether, on the table," she told MPs. "The prime minister is looking at all the options."

She added: "However, we are currently signatories to the convention and must abide by its rulings, and I believe that governments must abide by the law".

One Tory MP, Stewart Jackson urged May to be bold, adding that his constituents were fed up with waiting for action on the ECHR.

May suffered another setback in the case on Tuesday when the court of appeal refused her permission to take the Abu Qatada case to the supreme court. The appeal court judges ruled that the existing undertakings from Jordan did not provide sufficient protections for him to face a fair trial on his return.

The new treaty will trigger a fresh round of legal challenges from the cleric's lawyers that are likely to go all the way up to the court of appeal once again. May said Abu Qatada would remain in a high-security prison while it takes place.

The shadow home secretary, Yvette Cooper, said that 12 months ago May had promised Abu Qatada would soon be put on a plane: "We are back to legal square one again. In the past she has overstated the evidence, overstated her legal position, and overstated her legal strategy, which instead has failed. We hope that she has not done so again."

Cooper said there was uncertainty over whether the new treaty would actually clear the way for his deportation, pointing out that the special immigration appeals commission that blocked his removal said a change in the Jordanian criminal procedure code or an authoritative ruling by its constitutional court was needed to ensure that evidence obtained by torture was not admissible.

The text of the treaty includes article 27, which contains a stringent ban on the use of torture-obtained evidence. It places the onus on the prosecution to "prove beyond any doubt that the statement has been obtained out of free will and choice and was not obtained by torture". Abu Qatada's lawyers are expected to question the credibility of such guarantees.

May said the treaty included a number of fair trial guarantees that would apply to anyone being deported: "I believe these guarantees will provide the courts with the assurance that Qatada will not face evidence that might have been obtained by torture in a retrial in Jordan." She conceded that it will be up to the British courts to make the final decision, and that it was a process that could take many months.

The possibility of withdrawing on a temporary basis from the European convention on human rights emerged following a meeting in Downing Street between Cameron, May, the justice secretary Chris Grayling and the attorney general Dominic Grieve. No Lib Dem attended that meeting, but party members were given prior sight of May's Commons statement.

Conservative cabinet members have repeatedly used the Abu Qatada case to raise the possibility of withdrawing from the European convention on human rights. But without the support of the Liberal Democrats, such proposals can only be pursued through the Tory election manifesto.

A Lib Dem source said: "There is no proposal temporarily to withdraw from the European convention. We support the ECHR. We have seen reports about withdrawal, but we are not going to get drawn into press speculation."