Signaling a preference for a much smaller role for the federal government in public schooling, Senator Lamar Alexander, Republican of Tennessee, is introducing legislation on Thursday to revise No Child Left Behind, the Bush-era education law.

Coming two days after Senator Tom Harkin, Democrat of Iowa and chairman of the Senate education committee, released a 1,150-page education bill, the bill by Mr. Alexander, who is the ranking Republican on the committee, will compete with it.

The Alexander bill is described in its introduction as restoring “freedom to parents, teachers, principals, governors and local communities so that they can improve their local public schools.”

At less than one-fifth the length of Mr. Harkin’s bill, Mr. Alexander’s legislation would allow states to devise curriculum standards, tests, school rating systems and consequences for schools that fail to meet state goals with far fewer guidelines than are included in the Harkin bill.

Both bills would amend the half-century-old Elementary and Secondary Education Act that governs public schools receiving federal money to support the most vulnerable students.

“What they are really saying is they don’t trust parents and they don’t trust classroom teachers and states to care about and help educate their children, and they want someone in Washington do it for them,” Mr. Alexander said of Democrats in a telephone interview. “I just completely reject that.”

Congress has repeatedly failed to revise No Child Left Behind, which has been up for reauthorization since 2007. Starting last year, the Obama administration began granting waivers to relieve states from the law’s requirement that all students be proficient in math and reading by 2014. Under that provision, a majority of schools in the country were at risk of violating the law.

Mr. Alexander’s bill continues the current law’s requirement of testing students in reading and math in third through eighth grades and once in high school. All schools must report the scores and show how different racial groups, students with disabilities, those learning the English language and poor students perform on the tests.

The bill would require states to set standards that would allow students to be ready for college or a job “without the need for remediation.”

Neither Mr. Harkin’s nor Mr. Alexander’s bill mandates the content of academic standards. Mr. Alexander’s bill also does not prescribe what should be included in a state’s annual goals for student performance on tests; Mr. Harkin’s bill sets more guidelines.

The Alexander bill encourages, but would not require, states to set up teacher evaluation systems. It also does not mandate any turnaround measures for schools that fail to meet state goals, although it does list options including closing a school, replacing the principal or offering higher pay to recruit new teachers.

Mr. Alexander said he wanted to include a provision allowing parents to take public money and put it toward any public school or accredited private school of their choice. He said that he and Senator Rand Paul of Kentucky would be introducing an amendment to the bill once it reached the Senate floor to give vouchers to families to use federal dollars to attend private schools.

Some who had seen parts of the bill said that leaving all decisions to states and local school districts and allowing them to set goals could disadvantage students who already start school behind.

“The pressures from local superintendents and Realtors and everybody else to just make schools look good are overwhelming,” said Kati Haycock, president of the Education Trust, a nonprofit group that works to close achievement gaps for racial minorities and poor children. “And it is very hard to maintain a real focus, especially on the kids that have been behind.”

Others who had not yet seen the bill but were aware of Mr. Alexander’s preferences said that the law was meant to set conditions for receiving federal money.

“Nobody is forcing a state to take this money,” said Charles Barone, policy director for Democrats for Education Reform, a group that pushes for test-based teacher evaluations and has battled teachers’ unions. “If they are not willing to do this they should just be honest about it and live without the money.””