In a Written Ministerial Statement to Parliament, Mr Heaton-Harris set out the final budget position for the current financial year.
It provides £14.2 billion to be spent by the Northern Ireland Executive, with more than half earmarked for health.
The Government will confirm this budget in legislation if a devolved government is not in place.
Mr Heaton-Harris also introduced the Northern Ireland (Interim Arrangements) Bill today, which allows current civil servant decision-making arrangements to continue until an Executive is formed.
The Bill also includes new powers for the Secretary of State to direct Northern Ireland departments to provide him with advice or consult on options to raise revenue or deliver sustainable public finances in the ongoing absence of NI Ministers.
Combined, these steps provide funding clarity and ensure governance will continue if an Executive is not restored before the current arrangements expire on 5 June.
The Secretary of State met Northern Ireland's party leaders today at Hillsborough Castle to provide an update on these points.
Mr Heaton-Harris said: "It should be for locally elected politicians to take this strategic decision-making to transform and modernise NI's public services.
"However, the approach taken in setting the budget and the provisions included in the Interim Arrangements Bill will ensure important work progresses if an Executive is still not in place."
Mr Heaton-Harris said it was clear that work needed to happen to get Northern Ireland's finances onto a sustainable footing. He said:
This situation exists despite the UK Government providing additional funding totalling £7 billion to NI since 2014, on top of extra funding provided through the Barnett formula.
I remain committed to protecting the interests of people in Northern Ireland, and will continue to do everything I can to help the Northern Ireland Parties to work together to make that happen.
The people of Northern Ireland deserve a stable and accountable devolved government that delivers for them.
