ALBANY, New York — Private and religious schools in New York face greater scrutiny after state education leaders approved rules Tuesday requiring them to prove their academic programs line up with those of public schools.

The unanimous vote by the Board of Regents follows several years of debate that began with complaints of children graduating from fervently observant Orthodox Jewish schools lacking basic academic skills. The rules apply to all of New York’s 1,800 nonpublic schools.

State law requires that instruction given in nonpublic schools “be at least substantially equivalent to the instruction” at public schools.

The guidance approved Tuesday outlines several ways that private schools can show they meet the longstanding mandate, including by using state-approved assessments or undergoing a review by the local school district.

Private schools that fall short of the threshold will be given time to adjust their instruction, state education officials have said. Those who may refuse to comply could lose state funding.

Supporters of some of the fervently observant Orthodox schools, called yeshivas, have opposed the rules as infringing on religious freedom and parental choice.