Gov. Andrew M. Cuomo will propose legislation to ease the debt burden of thousands of college graduates, an administration official said.

Under the governor’s proposal, to be unveiled in his State of the State address on Wednesday, the state would cover two years of loan payments for graduates of New York State colleges who make less than $50,000 a year, continue to live in the state and are enrolled in the federal Pay as You Earn program, said the official, who spoke on the condition of anonymity because the proposal has not been released.

Roughly 60 percent of students who graduated from public and nonprofit colleges in New York in 2013 took on debt, and the average amount was $26,381, according to a report by the Institute for College Access and Success. The report did not include graduates from for-profit colleges, who generally accumulate more debt.

The governor’s office projects that up to 7,100 people would benefit in the program’s first year, increasing to 24,000 by 2020, as more students hear about the program and enroll in Pay as You Earn to qualify. The state would pay an average of $3,500 toward each participant’s loans.