There will be more talks at Stormont this week
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The prime minister is due to hold separate talks in London with the DUP, SDLP and Ulster Unionists.
Tony Blair is to discuss the prospects for a return to devolution, as efforts to end the political stalemate in NI.
The talks in Downing Street come amid speculation that Mr Blair is preparing another visit to Belfast, possibly within the next fortnight.
Later this week there will be talks at Stormont involving the political development minister David Hanson.
Those talks will be followed by more discussions in Hillsborough Castle next week involving the two governments and the parties.
BBC Northern Ireland political correspondent Martina Purdy said Mr Blair had two objectives.
"These are to kick-start the assembly and to tie Sinn Fein into the Policing Board," she said.
"The DUP last met Mr Blair in January and presented him with the party's plan to reopen the assembly.
"It involved phased devolution, with direct rule ministers keeping the functions of the executive until there was sufficient confidence to build power-sharing.
"The SDLP leader, Mark Durkan, has already rejected this out of hand, but Mr Blair will be hoping to find some common ground between the parties."