The prime minister believes "genuine progress" has been made in bringing Northern Ireland's political parties together to prepare for government.
Attempts will be made to restore the assembly by autumn
A spokesman said efforts to restore the assembly would be a "very important part of the agenda this autumn".
The government set 24 November as the deadline for agreement to be reached.
Mr Blair and the Irish leader Bertie Ahern are expected to meet the parties next month as part of the bid to restore the administration at Stormont.
Mr Blair's official spokesman said the next few months would be "one of the most important periods in Northern Ireland that we have seen for some time".
"This autumn will reflect that and the level of the meetings we have will reflect that," he said.
"We have seen some genuine progress in terms of the parties taking the preparation for government seriously."
The spokesman said co-operation would now "need to be taken to a new phase".
"A very important part of that will be two Independent Monitoring Commission reports, one on the normalisation process which will come probably before too long and the second, its report on paramilitary activity, which is due in October," he said.
"We have approached this in a methodical, patient and painstaking way and I think that does allow a basis for moving forward this autumn - but that will be for the parties to decide."
Devolved government was suspended over allegations of a republican spy ring.
The court case that followed collapsed and one of those involved, Denis Donaldson, later admitted working as a British agent.
Direct rule from London was restored in October 2002 and has been in place since.
The Preparation for Government Committee was set up to identify obstacles to the return of devolution. It has been meeting over the summer months.