Sinn Fein leader Gerry Adams announced on Irish television on Sunday that he plans to meet with Northern Ireland police chief Hugh Orde to deliver the demand in person.
"This is a crucial meeting in which we will be expecting Mr Blair and his chief constable to deliver for us on demilitarising republican heartlands," as promised in a joint London-Dublin agreement last year, Adams said on RTE public television.
Earlier on Sunday, Adams received a phone call from US President George Bush, who offered to mediate in the Northern Ireland conflict.
Bush had called Ian Paisley, the leader of the Democratic Unionist Party (DUP) - which supports continued British rule in Northern Ireland - to make the same offer on Friday.
The DUP never embraced the Good Friday pact - which sought to create a power-sharing administration in Belfast - after refusing any compromise with Sinn Fein.
Wheeling or dealing?
But Britain and Ireland are trying to push Paisley's DUP into agreeing to share power now - a previously unthinkable alliance.
Protestant unionists politicians, who support British rule, and their Catholic republican counterparts, who want a united Ireland, are studying an Anglo-Irish peace plan to revive home rule.
"We will be expecting Mr Blair and his chief constable to deliver for us on demilitarising republican heartlands"
Sinn Fein party leader
Adams said he believed his Protestant rivals were ready to agree to a peace deal.
"I think he [Paisley] will do a deal," Adams told BBC Television. "He wants to do a deal on his terms. He has to do a deal on terms that are acceptable to the rest of us," he added.
Sinn Fein's political spokesman, Gerry Coleman, told Aljazeera.net on Monday that the party is also preparing to inform US politicians and citizens of atrocities carried out in Northern Ireland by the British army and police.
Named after the Irish words for "the truth" (An Fhirinne), relatives of victims and two Sinn Fein party members hope to raise awareness "of state sponsored violence and demand the truth from the British Government on its policy of state sponsored violence in Ireland", Coleman said.
Sinn Fein also plans to build a database of documents that prove victim's stories and accounts of experiences of British atrocities in Northern Ireland and help those who wish to pursue their cases through the courts, he added.