State high school valedictorians and salutatorians would get free tuition to public universities under a budget plan the University System of New Hampshire revealed on Friday.

“We want to send a signal to those students who are first or second in their class that we would like them to stay here,” said Todd Leach, chancellor of the system that includes the University of New Hampshire, Plymouth State University, Keene State College and Granite State University.

The university system presented its budget plan to Gov.-elect Chris Sununu on Friday, asking for a 12 percent funding increase from the state over the next two fiscal years.

Leach said the system could freeze in-state tuition, offer free tuition to top students and create new scholarships for students studying science, technology, engineering and math with $182 million from the state. That’s $20 million above the current funding level.

“We do want more students to be able to afford a USNH education,” Leach said.

Reining in higher education costs and student debt has become a top priority of lawmakers and policy officials, as New Hampshire consistently ranks among the worst in the nation for college affordability.

The state has some of the highest in-state tuition rates for public universities in the country, according to the college board. And graduates of New Hampshire institutions had the highest debt load nationwide in two of the last three years, according to the Project on Student Debt.

Likewise, the state has the lowest per capita public support for higher education in the nation.

The university system was one of several state entities that presented its budget request during hearings that are scheduled to extend into next week. Sununu will unveil his two-year spending plan in February and indicated on Friday the tuition freeze is a “realistic possibility.”

“What they put on the table is a great starting point,” said Sununu, a Republican.

The university system is hoping the program will retain more New Hampshire students in-state, Leach told outgoing Gov. Maggie Hassan and Sununu. New Hampshire has the highest percentage of high school graduates who leave the state to go to four-year college, he told them.