Home Secretary Theresa May has said there "more work to do" as she arrived in Jordan for talks over the deportation of radical cleric Abu Qatada.
Mrs May is expected to remain in the country until Wednesday, a Home Office spokeswoman said.
Qatada, described by a judge as Osama bin Laden's right-hand man in Europe, has been released from jail under a 22-hour curfew while the Government seeks assurances that evidence gained through torture would not be used in any trial against him if he were sent back.
The 51-year-old cleric could be freed from his bail terms in just three months if Mrs May fails to show significant progress is being made in the talks.
Her visit comes after she said Security Minister James Brokenshire led "useful discussions with the Jordanian authorities" last month.
"The UK and Jordan remain committed to ensuring that Abu Qatada must face justice and are pursuing all options with regard to his deportation and it is my intention to travel back to continue those negotiations," Mrs May said after Mr Brokenshire returned to the UK.
Qatada was released from Long Lartin high-security jail in Evesham, Worcestershire, on February 13 after applying for bail when human rights judges in Europe ruled he could not be deported without assurances from Jordan that evidence gained through torture would not be used against him.
The Strasbourg-based European Court of Human Rights ruled that sending Qatada back without such assurances would be a "flagrant denial of justice".
Mr Justice Mitting, chairman of the Special Immigration Appeals Commission, then ruled that Qatada should be bailed after six and a half years in custody and gave the Home Secretary three months to show significant progress had been made in the talks or risk Qatada being freed without conditions.
Qatada was let out under some of the toughest conditions imposed since the September 11 terror attacks.
He is free to leave his London home for just two one-hour periods each day, is banned from taking his youngest child to school, and cannot talk to anyone who has not been vetted by the security services.
He is also banned from visiting mosques, leading prayers, giving lectures or preaching, other than to offer advice to his wife and children at his home.
Qatada, also known as Omar Othman, was convicted in his absence in Jordan of involvement with terror attacks in 1998 and has featured in hate sermons found on videos in the flat of one of the September 11 bombers.
Since 2001, when fears of the domestic terror threat rose in the aftermath of the attacks, he has challenged, and ultimately thwarted, every attempt by the Government to detain and deport him.
Speaking in Jordan, Mrs May said: "We and the Jordanian government will continue to work together to progress this case.
"Jordan has made significant human rights advances, including changes to its constitution. Sadly the Court at Strasbourg failed to recognise this.
"Talks today have been positive but we have more work to do in getting the kind of assurances that will allow us to deport Qatada once and for all.
"This case has gone on for over a decade and I want to bring it to a satisfactory end soon."
Justice Secretary Kenneth Clarke told BBC News: "I haven't been in touch with the Jordanian government myself.
"Obviously there is a problem with torture in that country, and I know that Theresa is extremely anxious to get credible assurances from the Jordanians that, if they put him on trial, there won't be evidence used against him that has been obtained by torture.
"That's a long-standing principle of human rights law. The British courts and European courts, every country that adheres to the European Convention on Human Rights is highly sensitive about torture.
"You can't have a system of justice with torture involved.
"She got good assurances from the Jordanians about Abu Qatada himself not being tortured and the court in Strasbourg accepted that.
"I hope she's successful in getting the assurances she is now seeking about the trial."