The British and Irish governments must deliver the “promised financial package”, Conor Murphy has said.
The new finance minister said the local parties had “done their portion by restoring the power-sharing executive”.
“The two governments must now honour their pledge and add the funding needed to deliver on the New Decade, New Approach document, ” he said.
Sinn Fein and the DUP, together with the SDLP, UUP and Alliance, re-entered devolved government on Saturday.
Stormont’s power-sharing coalition, led by the DUP and Sinn Fein, collapsed in January 2017.
After three years of deadlock, NI Secretary Julian Smith and Irish tanaiste( deputy prime minister) Simon Coveney publicized details of a draft deal to restore devolution on Thursday.
The DUP and Sinn Fein subscribed the deal to restore Stormont’s political academies.
Mr Murphy, a Sinn Fein MLA, said the deal contained “ambitious commitments for public services and workers”.
“To deliver these commitments, the authorities concerned pledged a substantial injection of funding, in addition to being the block subsidy, ” he added.
BBC News NI Economics and Business Editor John Campbell said he understood there was now some nervousness among the parties and officials about exactly how much coin will be on offer.
“The deal was done without anyone being clear about the numbers so there is still much to be pinned down, ” he added.
“The subtext of Mr Murphy’s statement is: ‘The government’s have raised public expectations and if they don’t come up with the currency the honeymoon will be terminated very quickly.'”