She says the issues dividing the parties are "relatively small in number"
The British Prime Minister Theresa May says she believes devolved government for Northern Ireland at Stormont can still be achieved.
Mrs May held talks with delegations from both Sinn Féin and the DUP in London.
The two parties have been locked in talks with no sign of agreement.
The Stormont Executive has not sat since January.
Speaking after the meeting at Downing Street, Mrs May said: "I made clear the determination of this government to re-establish the fully functioning, inclusive devolved administration that works for everyone in Northern Ireland.
"I also reiterated our steadfast support for the Belfast Agreement and its successors.
"For their part both the DUP and Sinn Fein expressed their commitment to seeing Stormont back up and running.
"From our discussions it is clear that the issues dividing the parties are relatively small in number, focusing mainly around culture, legacy, identity and the future stability of the devolved institutions.
"While not in any way underestimating the challenges involved, I believe that a way forward can be found and an agreement reached.
"It is therefore imperative that the parties re-engage in intensive discussions next week aimed at resolving the outstanding issues so that the Assembly can meet and an Executive be formed."
It comes as Westminster has moved to introduce a budget for Northern Ireland from London.
The Financial Times says the stg£10.6bn (€11.97bn) budget is expected to pass the Houses of Commons and Lords, and enter into force later this week.