U.S. Education Secretary John B. King Jr. is pushing new regulations that would designate public schools in which large numbers of students refuse to take Common Core tests as in need of improvement.

The proposals are drawing criticism from those in New York who have opposed the tougher exams and other education reforms, which King championed when he was the state’s education commissioner. They are available for public comment on the U.S. Education Department’s website.

The regulations, which the state Board of Regents discussed Monday for the first time, hit a particular nerve on Long Island because of sweeping test boycotts by students in grades three through eight, driven by both parents and educators. In April, more than 50 percent of eligible students in Nassau and Suffolk counties were pulled out of tests in English language arts and math.

The secretary, during a teleconference last week with reporters, noted in response to a question that federal law requires at least 95 percent of eligible students to participate each year in state testing. Such participation, he added, is especially vital in tracking the performance of students of color, who have tended to score low in the past.

“We feel it’s important, because we feel teachers and parents need good information about children’s progress,” said King, who is black and often talks about his childhood school experiences in Brooklyn.

Some regional education leaders said that King’s latest proposals are reminiscent of policies that he and other state officials pushed from 2011 to 2015, which sought to make tests more rigorous and tied teachers’ and principals’ performance evaluations to test scores.

Those policies proved widely unpopular with parents and teachers and helped spark the record-setting boycotts, which began with tests given in spring 2013 and have gotten bigger each year since.

Now, local leaders contended, King in his federal role is continuing to promote rules that would increase pressures on public schools and fuel resentments among teachers and parents.

“It’s bizarre when you think about it, that a school would be punished for decisions taken by parents, which is their right to do,” said Carol Burris, a former principal of South Side High School in Rockville Centre.

Burris now is executive director of the Network for Public Education, a nonprofit national research and advocacy group based in Queens, that opposes King’s latest proposals.

Betty Rosa, the Regents chancellor, said in answer to a reporter’s question that the board is more concerned with getting federal financial assistance for the state’s schools than in how schools may be labeled under the new federal guidelines. The new regulations would not take full effect until the 2017-18 academic year.

“There’s a whole wait-and-see situation,” Rosa said.

One result of the Island’s record-setting boycott is that the great majority of the region’s elementary and middle schools fall short of the federal 95 percent participation standard.

King’s proposed regulations would address such situations in two major ways. For starters, all schools would be assigned “summative” ratings — for example, letter grades such as A, B, C, D or F, or categories such as “Excellent” or “Failing” — that assess their academic performance according to a combination of criteria such as test results and graduation rates. Each state would decide on the form its ratings would take.

As a follow-up, schools with high opt-out rates could see their ratings lowered and be required to come up with strategies for improving test participation. Individual states could develop their own approaches to achieving that goal, as long as the federal agency adjudged their methods were equally rigorous.

U.S. Education Department officials already warned in December that schools with test-participation rates below 95 percent risked loss of federal financial aid. King, asked during Thursday’s teleconference if that policy remains in effect, did not answer directly but voiced confidence that states’ efforts to boost exam participation would eventually succeed.

The proposed new federal regulations are geared to carrying out a new law — the Every Student Succeeds Act, or ESSA, signed by President Barack Obama in December. The law spells out academic requirements for schools and provides for nationwide distribution of more than $14 billion in annual education funding.

King’s efforts were praised by Stephen Sigmund, executive director of High Achievement New York, a Manhattan-based coalition of business groups and others that support Common Core standards.

“All of us — teachers, parents, students, and even those opposed to state assessments — should be working together to find ways to strengthen how we track student progress,” Sigmund said. “We support Secretary King’s efforts to innovate in a system that, for far too long, turned a blind eye to students who were not being prepared for successful 21st century careers.”

The public can comment on the draft regulations until Aug. 1 by going to regulations.gov and searching for “Elementary and Secondary Education Act of 1965, As Amended by the Every Student Succeeds Act: Accountability and State Plans.” After that date, the new rules will be subject to amendment and final approval.

The Every Student Succeeds Act replaced the No Child Left Behind law, an initiative of George W. Bush when he was president. The new law retains the annual testing requirements of the old statute, but in other ways returns to individual states many of the powers formerly exercised by King’s predecessor, former Education Secretary Arne Duncan.

ESSA, for example, bans federal officials from requiring states and school districts to rate the job performance of teachers and principals, or to base such ratings on test scores. However, states can continue doing that on their own — as New York has, although most of the evaluation system currently is on hold under a moratorium until the 2019-20 school year.

Recently, Republican leaders in Congress charged that King’s draft regulations would violate the new law by reasserting federal authority in areas reserved for state control.

Sen. Lamar Alexander (R-Tenn.), chairman of the Senate Education Committee, who supported King’s appointment as secretary in March, said at a public hearing two weeks ago that the secretary “invented out of whole cloth a so-called summative rating system that’s nowhere in the law.”

Michael Hynes, superintendent of the Patchogue-Medford schools and a local leader of the movement against using test scores in evaluations, agreed with those who see the secretary’s plan as an attempted reassertion of a failed federal role.

“Federal overreach should be stopped in its tracks,” Hynes said. “To put so much weight into a score doesn’t make any sense. There are other things we should be focusing on, such as social and emotional development.”

King has responded that the draft regulations provide flexibility for states, which ultimately will decide which route to take in promoting test participation.

The secretary has won backing from senior Democrats in Congress, including Sen. Patty Murray (D-Wash.), who said King’s “strong regulations” would help boost the educations of “kids of color, kids with disabilities and kids learning English who too often fall through the cracks.”

Rep. Robert C. Scott (D-Va.), the ranking minority member on the House Committee on Education and the Workforce, commended King, saying the proposed regulations “fulfill the federal obligation to protect and promote equity, ensuring that ESSA implementation will uphold the civil rights legacy of the law.”