On Wednesday, Mr Brown said he believed agreement could be reached and that the parties would have another two days to consider the proposals.
He said that if there was no agreement, then the two governments would publish their plans.
The prime minister said that he believed that the devolution of policing and justice could happen at the start of May.
Speaking on the BBC'S Evening Extra programme DUP deputy leader Nigel Dodds said: "We're not going to be held to ransom by the demands of any party by false or artificial deadlines, we won't be bullied.
"We will do what is right and proper and take our decisions in the best interests of the people who elected us and the people of Northern Ireland as a whole."
However, Sinn Fein policing spokesman Gerry Kelly said: "This is three years into the default of the DUP after the St Andrews Agreement which they signed up to.
"There has to be an end to people within the DUP trying to draw us back into what they see as unionist dominated institutions."
BBC Ireland correspondent Mark Simpson said that while "a deal is not impossible the departure of the two prime ministers inevitably reduces the momentum of the talks".
"In the words of one source, the air has gone out of the balloon," he added.
Speaking after talks at Hillsborough broke up, Mr McGuinness said: "We have not concluded a deal today and I am deeply disappointed about that. We intend to study the governments' statement."
He added that his party would not accept "citizens' rights" being subject to a "unionist veto" or an "Orange Order pre-condition".
The DUP leader, Peter Robinson, said his party would not accept a "second-rate deal" to suit "someone else's time-limit".
He added: "We are not prepared to buy a pig in a poke. We will do what is right for our community."
The Irish prime minister, Brian Cowen, said it was "unfortunate that the discussions had not been completed".
Further talks continued at Hillsborough Castle after the two prime minsters left, but it is understood that discussions finished about 1900 GMT.
Martin McGuinness said he was disappointed no deal had been reached.
The relationship between Sinn Fein and the DUP - Northern Ireland's two biggest political parties - has been strained for some time because they disagree about the timetable for the transfer of policing and justice powers from Westminster to Stormont.
Sinn Fein wants the completion of devolution to happen as soon as possible, but the DUP argues there must be unionist "community confidence" before powers are put in the hands of local politicians.
The "confidence" issue causing most division is over the handling of parades.
The DUP wants to scrap the Parades Commission, which puts conditions on some of the most contentious marches, but Sinn Fein has accused the party of giving the Orange Order a talks veto.
Are you in Northern Ireland? Do you think the talks will succeed? Send us your comments.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.