Sinn Fein president Gerry Adams has confirmed the party has agreed to accept the prime ministers financial offer on the devolution of policing and justice powers.
The decision was taken at a meeting of the party's officer board in Dublin.
"Yesterday we received from the British Government in writing the details of the financial package being proposed," Mr Adams said.
"The party's chief negotiator, Martin McGuinness, recommended to the officer board that we proceed on the basis of this financial package.
"The officer board accepted this recommendation and Martin McGuinness will inform the British Government of this in discussions in London on Tuesday.
"The process to transfer powers should now be completed quickly."
Before entering Number 10 for talks with Mr Brown, Mr McGuinness said he wanted the transfer of powers to take place "as soon as possible".
"What we now need to do is press on," he told reporters in Downing Street.
"This needs to be concluded."
Mr Robinson had entered Number 10 a few minutes before.
Meanwhile members of the Stormont committee examining the devolution of policing powers from Westminster have demanded sight of the financial deal the Prime Minister is offering.
The Assembly and Executive Review Committee has requested that DUP First Minister Peter Robinson and Sinn Fein Deputy First Minister Martin McGuinness release details of Gordon Brown's offer without delay.
SDLP representative on the ad hoc body Alex Attwood said it was unacceptable that Mr Robinson and Mr McGuinness had briefed their own parties on the contents of the package but had not yet informed Assembly members whose responsibility it was to look into the transfer of law and order functions.
"We now have a situation where OFMDFM negotiated this on behalf of the assembly and have now agreed that the first port of call will be their own parties and not the Assembly and Executive Review committee," he said.
"I just don't think that's a balanced and proper way to do business."
Northern Ireland police chiefs said while they had not seen details of the deal they were encouraged with the progress made toward reaching a settlement.
Mr Attwood's proposal asking for sight of the offer was agreed by majority vote with the DUP and Ulster Unionist members of the committee backing his request. Sinn Fein, however, opposed the suggestion.
Alex Maskey from the republican party said the committee had no right to make demands on the two ministers to release documents that had been sent to them.
"We may wish to ask them to share the substance with us but we can't direct them," he said.
He stressed that it was the First and Deputy First ministers who had the responsibility to take forward the negotiations with Downing Street and not the committee.
Mr Attwood acknowledged his point but added: "They shouldn't be allowed to take this forward without our involvement."
Former DUP Finance Minister Nigel Dodds said it was important that all the parties in the Assembly knew what was on offer.
"Ultimately there needs to be buy-in from everybody before there is a settlement," he said.
"That's clear and must be the case."
Alan McFarland, a UUP representative on the committee, said it appeared that every branch of the criminal justice system was being briefed on the details while he and his colleagues were still left in the dark.
"It seems this has been shared with everyone else in the criminal justice system and not the assembly," he said.
"But that's the way the DUP and Sinn Fein have been doing business since the very beginning."
© Press Association