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 health care staff calling for pay parity and safer staffing levels.
Mr Smith is holding a health summit with the parties on Thursday.
The summit is part of the overall process to restore Stormont.
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.
The total number of hospital appointments cancelled on Wednesday was 4,749.
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.
‘Unlikely that summit will yield breakthrough’
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 this meeting was always scheduled to take place this week.
As the parties wrangle their way through negotiations to try and restore Stormont, they will focus solely on health today, which in recent days has dominated their discussions anyway.
Perhaps the secretary of state believes a formal “summit” will 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.
It seems unlikely that any breakthrough will emerge at the summit, given Julian Smith is sticking to his position that it remains a devolved matter.
Health workers say they want to be paid the same as their counterparts in England, Scotland and Wales.
Pay parity between Northern Ireland and the rest of the UK ended in 2014 when the then health minister, Jim Wells, imposed a “degree of restraint” on pay for health care workers, due to financial challenges in the department.
Speaking earlier this month, Mr Wells said the decision had been “very difficult because the choice was very stark”, explaining that another increase in pay at the time could have led to redundancies or services being closed.
The issue has not been looked at again because Northern Ireland has not had a devolved government since 2017.
The political parties have been taking part in efforts to restore power sharing this week – but it is understood Thursday’s summit will focus solely on the health crisis.
Mr Smith is expected to tell the parties that the crisis in the NHS in Northern Ireland must be addressed as an “immediate priority”.
Industrial action also continues on Thursday, but not at the levels faced across Northern Ireland earlier in the week.