The secretary of state has said he does not want to get into a "blame game" with the Stormont parties about resolving the health sector crisis.
Earlier this week, party leaders urged Julian Smith to take control of the matter.
This followed unprecedented strike action by healthcare staff calling for pay parity and safer staffing levels.
On Thursday, Mr Smith met the parties to discuss health.
Party representatives were at the meeting, along with senior Stormont civil servants and the British government, but the discussions form part of the overall process to restore devolution.
Mr Smith is also expected to meet party leaders with Tánaiste (Irish Deputy Prime Minister) Simon Coveney at 17:00 GMT on Thursday.
Northern Ireland has been without an executive since January 2017, when the governing parties split in a row.
About 15,500 nurses in Northern Ireland staged a strike action on Wednesday in a dispute over pay and patient safety.
It follows weeks of industrial action by other healthcare workers over the same issues.
Major investment needed
The secretary of state said he wanted to be as "activist" as possible in getting the executive restored, but insisted he has no powers to intervene directly on health.
Asked if the British government would contribute funding towards health if the parties could reach consensus, Mr Smith said he was "expecting a number of financial requests" from the parties.
He added that he is already in touch with the Treasury in London.
Speaking after the summit, Sinn Féin's Pat Sheehan said nothing had changed as a result – but described the talks as "constructive and positive".
He added that solving the problems would need a major investment of funding and civil servants had outlined how much would be required, in broad terms, to do so.
Analysis: Breakthrough will have to wait
By Jayne McCormack, BBC News NI political reporter
Ears might prick up at the news of a health summit being convened, but government sources say the meeting was always scheduled to take place this week.
As the parties wrangle their way through negotiations to try and restore Stormont, they focused solely on health this morning, which in recent days has dominated their discussions anyway.
Perhaps the secretary of state believed a formal "summit" would focus minds.
But the parties argue that given the strike action happening away from the hill, an immediate response is required by the government, outside of the talks process.
Julian Smith is sticking to his view that it remains a devolved matter, so any bRead More – Source