Republicans in Congress have rolled out legislation that would sharply limit the power of the executive branch and shrink the role of the federal government in public education in a rebuke to the Obama administration’s influence over education from kindergarten through 12th grade.

Meanwhile, Senate Democrats have unveiled their own K-12 plan, which would cede more control to states but still maintain some federal oversight, especially of the worst-performing schools.

This is the latest attempt by members of Congress to rewrite No Child Left Behind, the main education law that sets conditions and requirements for every public school receiving federal funds to educate poor students and those with special needs.

No Child Left Behind was signed into law by President George W. Bush in 2002 and expired in 2007.

But despite several attempts — including one a little more than a year ago — and broad dissatisfaction among school leaders, teachers and parents with No Child Left Behind, Democrats and Republicans in Congress have been unable to agree on a new law.

All the bills introduced this week would get rid of the most unpopular aspect of No Child Left Behind — the provision known as annual yearly progress, which requires schools to make yearly progress toward a requirement that all students be proficient in math and reading by 2014. If they fail to make progress, schools are subject to steadily escalating punitive measures.

That goal of proficiency by 2014 came to be widely seen as unrealistic, and officials from state governors to school board members have been asking Congress to rewrite the law and replace the provision.

With Congress unable to agree on a new law, the Obama administration in 2011 began issuing waivers to states to free them from the requirements of No Child Left Behind. In exchange for waivers, states were required to adopt President Obama’s preferred education reforms.

That outraged Republicans on Capitol Hill, who accused Obama of meddling in public schools, an arena with a long history of local control.

In his bill, Sen. Tom Harkin (D-Iowa), chairman of the Senate Health, Education, Labor and Pensions Committee, would retain a central requirement of current law — that states test students in math and reading annually from grades 3 through 8 and once in high school. States would be required to make public those scores and the performance of students by race, disability and other categories. Those provisions are in the current law.

But Harkin’s bill would lessen the emphasis on standardized tests by letting states use portfolios or projects to assess student performance. And his bill would allow states to come up with their own strategies for improvement, except in cases of the worst-performing schools. Under current law, states must choose from among four “turnaround” strategies prescribed by the federal government.

Harkin’s bill would cut 20 programs and shift the funds to encourage schools to offer or expand arts instruction, physical education and early childhood education.

On Thursday, the committee’s ranking GOP member, Sen. Lamar Alexander of Tennessee, introduced his own proposal, which would sharply limit the involvement of the federal government. Alexander, a former Tennessee governor who served as education secretary under President George H.W. Bush, called the Democrats’ version “congested with federal mandates.”

Under the Obama administration, the Education Department has become “the national school board,” Alexander said in a statement.

Alexander’s bill would leave to the states decisions about how to measure student achievement, improve schools and gauge the performance of schools and teachers. His plan would replace 62 programs with two block grants that states could use to pay for local needs and priorities.

In the House on Thursday, Rep. John Kline (R-Minn.), who chairs the committee on education and the workforce, rolled out his proposal, which calls on states to set their own academic standards and decide whether schools are meeting them, as well as what to do about underperforming schools.

His plan would preserve the requirement that states test students in math and reading annually from grades 3 through 8 and once in high school but also would require regular testing in science.

Like the Senate Republican version, Kline’s bill would let states set their own academic standards, decide how well schools are performing and determine what to do about poor performance.

But that kind of autonomy presents problems for children, Democrats said.

Rep. George Miller (Calif.), the ranking Democrat on the committee and one of the authors of No Child Left Behind, said Kline’s bill “turns the clock back decades on student achievement, equity and accountability in American public education.”

The Senate committee will mark up its bill next week; the House committee will vote on its bill June 19.