Simon Hamilton said it was a "critical week for Northern Ireland".
If a draft budget for 2015/2016 is not agreed by Friday, Stormont will lose a £100m emergency loan from the Treasury.
The loan was designed to ease pressures for the remainder of this year. Under Mr Hamilton's plan, education is not spared the impact of savings.
Mr Hamilton said: "These are decisions that the executive has to face this week, and very much the decisions we make in respect of health and, I think, more importantly, education which, of course, has been protected this year from any cuts. But I don't think that should be the case for next year.
"But if we were to protect it, that means the size of the reductions in percentage terms for departments could be as high as 20% and I don't think that is something that is achievable. I don't think that is a credible plan."
The minister said negotiations this week would be difficult, but he was optimistic a deal could be agreed.
Mr Hamilton said £700m would be a "conservative enough estimate".
"The pressures we are facing are in excess of that and that necessitates tough choices on behalf of me and executive colleagues," he said.
"It is very, very difficult to take that sort of quantity of money out of our budget in Northern Ireland without there being difficult decisions."
His comments come after Northern Ireland Secretary Theresa Villiers said Stormont parties have been told that the job of resolving budget questions will be taken from them, unless they agree a draft budget by the end of the month.
Ms Villiers said that while there was some flexibility in the process of consultation, it was crucial the parties stuck to the timetable.
"Unless they get on and agree a draft budget, ultimately when we get to April, we'll end up with civil servants making the allocations on budgets," she said.
"We'll end up with a situation where Northern Ireland's elected leaders have the power to resolve budget questions taken from them.
"No-one wants that. We want democratic decisions taken over the budget and that's why they need to get on and get this draft budget agreed by the end of this month."
Northern Ireland's finance minister has proposed cuts of more than £700m to Stormont departments in a plan circulated to his executive colleagues.