Under the new rules, the government could withhold grants to the schools if it doesn't like what it sees in annual financial statements, Regan said as she released the results of a four-month review.
The new law would require the institutions to follow standard financial reporting practices.
"Accountability should not be left to chance — it must be law," the minister said. "The legislation will have teeth, up to and including the authority to withhold grants in extreme circumstances."
Regan said the government gives the universities about $500 million annually. By 2018, there will be a $50 million funding gap between what the universities require and what the government is able to pay, she said.
The review also found there was no appetite for closing or merging schools.
"Nova Scotians value our 10 institutions," she said. "They like the fact that ... they're located throughout the province and are economic drivers in their regions."
The previous NDP government also launched a review of the university system that resulted in a September 2010 report that said four schools were candidates for mergers. One of those schools, the Nova Scotia Agricultural College, merged with Dalhousie University in 2012.
Regan said her review also found universities want to continue setting their own tuition levels and they want a cap on those levels removed. As for students, Regan said they are calling for free university education or a tuition freeze.
The minister said any details about funding would not be released until the budget is tabled this spring.
However, she said it will be difficult for the government to increase funding.
"Simply put, the cupboard is bare," she said, adding that Nova Scotia taxpayers pay more to support their universities on a per capita basis than every other province except Newfoundland and Labrador.
Student leader Michaela Sam said she was disappointed with Regan's presentation.
"Not seeing support in terms of reducing tuition fees and increasing university funding really means that the Nova Scotia government is missing an opportunity for students ... and that's a failure," said the head of the Canadian Federation of Students in Nova Scotia.
Meanwhile, the government is changing a program that forgives student loans.
Under the changes, only students from Nova Scotia would be eligible for debt relief if they go to school in the province and graduate in a reasonable time prescribed by the government. For a person with a permanent disability, that means graduating in six to 10 years, while students without a disability would still have to graduate within four years.
There would be an exception for students who go to school outside the province for a program that is not offered in Nova Scotia.