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".
The Home Secretary pinned her hopes for ousting Abu Qatada from Britain on a fresh deal with the Jordanians.
A Tory MP and former government lawyer give their view on the UK potentially withdrawing from the ECHR to aid Abu Qatada's deportation.
The Government has been refused permission to take its fight to remove preacher Abu Qatada from the UK to the Supreme Court.