WASHINGTON — Facing a bipartisan backlash led by Republican lawmakers, the Trump administration is backing off a bookkeeping change that would have drastically cut federal funds for rural schools — at least for a year.

Betsy DeVos, the education secretary, will allow states to more easily qualify for funding under the Rural and Low-Income School Program, after hundreds of districts faced cuts when the department abruptly began using eligibility requirements it had not enforced in 17 years.

During a program review, the department discovered that schools had been receiving funding based on the number of students who qualify for free or reduced-price meals rather than poverty data from the census, as is required by law.

But Ms. DeVos determined that she had the authority to allow the use of alternative data for an additional year, said Angela Morabito, a department spokeswoman. The department has also proposed language for Congress to permanently change the data source in the law. “We hope they act quickly,” Ms. Morabito said.