The legal move follows a ruling by the Special Immigration Appeals Commission (Siac) that Qatada should not be deported to Jordan on the grounds that evidence gained through torture could still be used against him, which would deny him the right to a fair trial.
The Home Office applied to Siac for permission to appeal against this decision, but it was turned down.
As a result, the Government has applied to the Court of Appeal.
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.