The House of Representatives on Tuesday overturned two key education regulations enacted under President Barack Obama, a move that could change how state officials evaluate school performance and roll back requirements for programs that train new K-12 teachers.

The two votes under the Congressional Review Act, a measure that allows lawmakers to repeal regulations within 60 days of their enactment, aim to curtail the authority of federal officials over educational decisions on the state and local level. To nullify the rules, the Senate must also vote to overturn them and the president must sign the resolutions into law.

The teacher-preparation rule, meant to ensure that new teachers are ready for the nation’s classrooms, require each state to issue annual ratings for teacher-prep programs within their borders, with poor-performing programs losing eligibility for some federal student aid. It stemmed from the Higher Education Act. It was overturned by a vote of 240 to 181.

The school accountability rule — which lays out how states should judge which schools are serving students well and which are struggling and need help — stemmed from a bipartisan law, the Every Student Succeeds Act. But many members argued that the previous administration stretched the confines of the law in crafting their regulations.

“Both in principle and in practice, we believe that education is most successful when states, local leaders, and hey, this may be a crazy thought — moms and dads — have decision-making power over education in their own communities,” House Speaker Paul D. Ryan (R-Wis.) said in a statement Tuesday.

Terry W. Hartle, senior vice president for government and public affairs at the American Council of Education, said the preparation rule aimed to connect colleges and universities to every elementary and secondary school in their state.

“This was one of those ideas that makes sense in theory, but not in practice,” Hartle said, adding it would have cost as much as $500 million to implement in California alone. “The notion of a one-size-fits-all federal approach never made any sense.”

The House overturned the accountability regulations by a vote of 234 to 190. The Obama administration wrote them to implement the successor to No Child Left Behind law, which shifted much authority over public education from the federal government to the states.

Civil rights groups see the regulations as essential for protecting the nation’s most vulnerable students, but a strange-bedfellows alliance of Republican lawmakers and teachers unions accused the Obama Education Department of writing rules that had no basis in the law passed by Congress.

For example, the regulations give states several options for addressing schools with low participation rates on annual standardized tests, a situation that has become more common with the rise of the “opt-out movement” of parents who refuse to let their children sit for tests. All of the options are designed to ensure that such schools feel enough pain, through penalties to their ratings, that they come into compliance.

Civil rights advocates believe such measures are necessary to keep schools from hiding the poor performance of disadvantaged students, but Republicans called it an executive overreach.

The effort to undo the regulations comes as states are in the middle of writing school accountability plans based on the new regulations; the first deadline for states to submit those plans to the Education Department is April 3. If the effort succeeds, then the application the states are completing — which is part of the regulations — will be null and void, leaving questions about how and when states are supposed to complete their plans.

Rep. Robert C. “Bobby” Scott (Va.), the ranking Democrat on the House education committee, said in a statement that the effort to nullify the accountability regulations “undermines the bipartisan intent of Congress, leaves states in the lurch by causing confusion and delays for submission of ESSA plans, and guts equity protections for vulnerable students the law is intended to serve.”

Chris Minnich, executive director of the Council of Chief State School Officers, which represents state superintendents of education, said he is not taking a position on the rollback effort. But he said it’s important that new Education Secretary Betsy DeVos — who was narrowly confirmed Tuesday — move quickly to provide states with clarity.

“There’s obviously some things about the regulations that we’d like to see changed but in the end, what’s most important is that the secretary be clear with the states what’s next,” Minnich said. “States are already planning, they have good plans in place, they’re starting to come together — and we can’t have this slow them down.”

On Tuesday, the House also overturned a Bureau of Land Management planning rule, by a vote of 234 to 186, that the Obama administration said would provide greater public and scientific input into federal land management decisions. Congressional Republicans said it constrained the ability of state and local officials to make land in their areas available for development activities.