Radical cleric Abu Hamza has launched a last-minute High Court bid to avoid extradition to the United States.
A second terror suspect, Khaled Al-Fawwaz, has also mounted a legal challenge. It is expected that their applications will be heard as a matter of urgency, but no date has yet been set.
The move for injunctions was confirmed by a spokeswoman for the Judicial Office.
The latest legal action comes after Europe's human rights judges this week rejected a bid for an appeal by Hamza and four other terror suspects, paving the way for their extradition. A panel of five judges threw out their request to the Grand Chamber of the European Court of Human Rights.
Hamza, who was jailed for seven years for soliciting to murder and inciting racial hatred, has been fighting extradition since 2004.
Computer expert Babar Ahmad, who was also subject to this week's ruling, has been held in a UK prison without trial for eight years after being accused of raising funds for terrorism.
After the ruling, the Home Office said Hamza and Ahmad, with Seyla Talha Ahsan, Adel Abdul Bary and Al-Fawwaz, would be "handed over to the US authorities as quickly as possible". Between 1999 and 2006, the men were indicted on various terrorism charges in America.
Hamza has been charged with 11 counts of criminal conduct related to the taking of 16 hostages in Yemen in 1998, advocating violent jihad in Afghanistan in 2001 and conspiring to establish a jihad training camp in Bly, Oregon, between June 2000 and December 2001.
Ahmad and Ahsan are accused of offences including providing support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country. Bary and Al-Fawwaz were indicted - with Osama bin Laden and 20 others - for their alleged involvement in, or support for, the bombing of US embassies in Nairobi and Dar es Salaam in 1998. Al-Fawwaz faces more than 269 counts of murder.
A Home Office spokeswoman said: "The European Court of Human Rights ruled there was no bar to the extradition of these men. We will continue working to ensure they are handed over to the US authorities as soon as possible."