Northern Ireland Secretary Peter Hain has been holding separate meetings with the DUP and Sinn Fein.
Tony Blair and Bertie Ahern speaking in Brussels
Mr Hain said it was up to the parties to decide if they would sign up to power-sharing by the 26 March deadline.
The talks come as the British and Irish prime ministers urged political leaders not to miss an opportunity of "historic proportions" to restore power-sharing.
Tony Blair said the election was called on the understanding that a devolved government would be established.
Speaking alongside Bertie Ahern at the EU Council meeting in Brussels, Mr Blair welcomed the election result.
"I think now is the moment in Northern Ireland that we can get down to business," he said.
"I think the parties that have been successful can take charge in Northern Ireland."
Mr Blair said the electorate had shown "real leadership" by signalling that they wanted "genuine power-sharing".
Questioned on whether the March 26 deadline for striking a devolution deal was final, Mr Blair responded: "The date's there and the reason it was called is so people would go into government."
He added: "People want to see elected politicians deliver on issues that matter to Northern Ireland."
Mr Ahern said it was the "first time Northern Ireland's been able to have that kind of election on the kind of issues the PM and I deal with every day".
"It's a really good achievement and I'm glad that it's happened," he added.
Sinn Fein has warned that failure to meet the deadline means that the British and Irish governments must implement their plan of increased cross border co-operation.
Party president Gerry Adams told a press conference: "We look to both governments to accept what the people overwhelmingly voted for yesterday, which is for local politicians who sought a mandate to exercise that mandate in the institutions of the Good Friday Agreement."
Speaking after meeting Mr Adams and Martin McGuinness, Mr Hain said Northern Ireland's politicians had reached a point where they must either "put up or shut up" over the return of devolved government.
He said: "It is either a functioning executive with powers devolved on March 26 or it's dissolution and the politicians stop getting paid, Stormont closes down and we pack up Northern Ireland politics, maybe for years to come.
"I will be writing to the party leaders and to the new elected MLAs later today explaining what the St Andrews legislation means because some seem unaware of it."
DUP deputy leader Peter Robinson also held a private meeting with Mr Hain who was then due in Ballymena for more talks with DUP leader Ian Paisley.