Mr Seamus Mallon has provided the British Prime Minister, Mr Blair, with a list of seven specific requirements that should be met if there is to be hope of the SDLP endorsing the new Police Act.
These include a request for independent judicial inquiries into the controversial killings of Pat Finucane, Robert Hamill and Rosemary Nelson, which would not be part of the Act's implementation plan due to be published within two weeks.
The SDLP and Sinn Fein have complained that the Act denies the Policing Board powers of retrospective inquiry, but were Mr Blair to set up such investigations it would help meet some nationalist concerns about past RUC actions.
Mr Mallon said while the inquiries were outside the scope of Patten and the Act they were vital to nationalist confidence in the new policing system.
The Deputy First Minister described in specific detail to Mr Blair in Downing Street on Wednesday what is demanded of the British government to help persuade nationalists that they should join the new Police Service of Northern Ireland.
Asked if he was more hopeful of nationalist concerns being met on policing after his meeting with the British Prime Minister, Mr Mallon replied: "I would not qualify this in terms of hope or despondency.
"But what I believe to be the case is that there is a growing [Downing Street] understanding of why the nationalist community and the SDLP are so concerned to get clarity and certainty about how things need to be managed.
"I do know he [Mr Blair] shares my very firm view that unless we get this policing issue right then there will be a very substantial negative impact on the workings of the agreement elsewhere.
"I do not have any doubt that he shares that view, and if so then I would believe he would share my hope that we can prevent a very deep crisis on this issue," Mr Mallon said.
He asked Mr Blair for "clarity and certainty" that if the Policing Board failed to agree on emblems and flags for the new service any subsequent decisions on symbols by the British government would meet the Patten recommendation that they be neutral of the British and Irish states.
He also sought guarantees that the Special Branch would be subsumed into the general crime division of the force.
