The two leaders met at Downing Street
It is vital Stormont politicians continue their work on devolving justice powers to Northern Ireland, Prime Minister Gordon Brown has said.
He said the British and Irish governments would do whatever it took to support their efforts.
The talks came as speculation mounts that agreement between the DUP and Sinn Fein on the issue could be closer.
Mr Brown said he was hopeful that deal could be reached, however, he added that nothing was yet certain.
"We take nothing for granted this has been a period of great turbulence in the politics of Northern Ireland," the prime minister said.
Mr Cowen said outstanding issues between the parties were ready for agreement.
He said: "The issues have been under discussion for some time and in our view are ready for agreement and resolution."
The talks between the two leaders took place in London.
Earlier, the Northern Ireland deputy first minister said "earnest efforts" were being made to find a way through the impasse.
Martin McGuinness said critical discussions were taking place and he would not be drawn on the detail.
Later on Thursday, Sinn Fein President Gerry Adams said talks with the DUP on the devolution of policing and justice remain at a serious, focused and sensitive point.
Mr Adams, who is at Stormont castle, said senior party members had cleared their schedules and they were there ''to do business''.
Martin McGuinness said critical discussions were taking place
A meeting of the party's Ard Choimaile has been postponed until the party's negotiators are in a position to put something definitive to it.
The DUP leader Peter Robinson who has stood aside briefly to deal with his wife Iris's mental illness is expected to attend the talks.
Meanwhile, SDLP leader Mark Durkan said it seemed that "a humbler DUP" had found "a clearer perspective" on the devolution of justice and policing.
Speaking after a meeting with Mr McGuinness, Mr Durkan said that the issue now is "how decisive they will be about delivering completion."
He added that the SDLP will not be "making it harder for any party to do the right thing from here and now."
The question of how to deal with Orange Order parades is believed to be a sticking point between the parties.
Sinn Fein is resisting DUP efforts to replace the Parades Commission.
The DUP wants an alternative way to adjudicate on contentious marches along the lines of interim proposals produced by a group headed by Lord Ashdown.
It is thought the DUP and Sinn Fein could try to reach a compromise position or agree to resolve the issue at a future date.
Alliance Party leader David Ford held talks with the DUP on Wednesday, a meeting which he described as "positive and useful".
However, he added there was "clearly still a lot of work to be done" before an agreement on policing and justice could be reached.