When asked if a temporary withdrawal from the European Convention on Human Rights was a possibility, to help facilitate the deportation of Abu Qatada, Mrs May said:
We should have all options - including leaving the convention altogether - on the table. The Prime Minister is looking at all the options. That is the only sensible thing to do.
Shadow home secretary Yvette Cooper has said she welcomes the work the Home Secretary is continuing to do to get Abu Qatada deported and the further assurances sought from Jordan.
However, she added: "She will know that the history of Home Office problems in this area mean that serious questions remain.
"The question for the house and the Court will be whether it meets the specific test that the court has set".
"We wish her well with this mutual legal assistance treaty and we hope that it will work.
Mrs Cooper also suggested a debate and vote should be held to "demonstrate the strength of support there is across this house".
Home Secretary Theresa May has said she believes the new treaty with Jordan would give the Government "every chance of succeeding" in its aim to deport Qatada to the country.
The Home Office has released a picture of the Home Secretary Theresa May signing the treaty with the Jordanian Ambassador to the UK, Mazen Homoud, that she hopes will facilitate Abu Hamza's deportation.
A new agreement between the UK government and Jordan also includes a number of fair trial guarantees which will apply to anyone deported from either country, the Home Secretary has confirmed.
Theresa May said: "I believe these guarantees will provide the courts with the assurance that [Abu] Qatada will not face evidence that might have been obtained by torture in a retrial in Jordan".
Yesterday, the Government was refused permission to take to the Supreme Court its fight to remove Qatada from the UK.
In March, the Court of Appeal backed an earlier ruling that the radical cleric could not be deported over fears that evidence obtained through torture would be used against him.
The Home Secretary has confirmed that she has signed a "comprehensive mutual legal assistance" agreement with Jordan which could aid efforts to deport radical cleric Abu Qatada.
Theresa May said the agreement is "fully reciprocal and offers considerable advantages to both countries, and reflects our joint commitment to tacking international crime".
"I believe that the treaty we have agreed with Jordan - once ratified by both parliaments - will finally make possible the deportation of Abu Qatada.
"But as I have warned the House before, even when the treaty is fully ratified, it will not mean that Qatada will be on a plane to Jordan within days".
The Home Secretary Theresa May has made a statement on efforts to deport the radical cleric Abu Qatada.
She said the government will seek permission to appeal to the Supreme Court after the Court of Appeal rejected the Government's request to go the court in its fight to extradite Qatada.
Home Secretary confirms government will seek Supreme Court appeal over Abu Qatada deportation #Qatada
The Home Secretary, Theresa May will make a statement to the Commons today, after the Court of Appeal rejected the Government's request to go the Supreme Court in its fight to extradite radical cleric Abu Qatada.
The Government could still ask to appeal to the Supreme Court directly, but the request is less likely to be successful than if it had the backing of the Court of Appeal. No other legal options remain if the Supreme Court decide not to hear the case.