A Senate panel voted 15 to 7 Thursday to reduce the role of the federal government in overseeing the nation’s 100,000 public schools as part of a revamping of No Child Left Behind, the key education law.

The government would stop supervising the performance of 95 percent of the nation’s schools under a bipartisan bill crafted by Sen. Tom Harkin (D-Iowa), chairman of the Health, Education, Labor and Pensions Committee, and the ranking Republican, Sen. Mike Enzi of Wyoming.

Only 5 percent of a state’s worst-performing schools — often known as “dropout factories” — would be subject to federal oversight under the measure.

Another 5 percent of schools — those with the greatest achievement gap between students of different racial groups — would also be required to make improvements under the proposed legislation, but states would determine how to intervene in those schools.

The legislation would drop requirements that all public schools meet yearly achievement goals or face federal sanctions.

Republicans on the committee pushed to further shrink the federal role and return more authority to states and local districts. Democrats argued that the federal government must maintain oversight to ensure that struggling children get the attention and resources they need.

In an unusual political pairing, teachers unions and conservative Republicans pressured Harkin to scrap a provision that would have required schools to evaluate teachers using student test scores, classroom observations and other methods. Unions have been adamant that student test scores do not adequately reflect teacher performance.

“For 95 percent of schools, Washington is going to get out of the business of deciding who is succeeding and who is failing,” said Sen. Lamar Alexander (R-Tenn.), a committee member and former education secretary. He was among three Republicans — including Enzi and Sen. Mark Kirk (R-Ill.) — who joined with Democrats to approve the bill.

It now heads to the full Senate for a vote.

Harkin said that he wanted to keep the teacher evaluation requirement and to require states to set annual goals for student achievement but that he made the concessions to win the backing of Republicans.

“I refuse to let the perfect to be the enemy of the good and for my own views to take precedent over the needs for bipartisan legislation,” Harkin said.

The bill would retain a key provision of No Child Left Behind, which requires schools to test students annually in reading and math in grades three through eight and once in high school. Schools would also be also required to break down those results by gender, racial group and English ­language ability.

Sen. Rand Paul (R-Ky.), elected last year with support from the tea party movement, wanted to get rid of that, too. He unsuccessfully tried to persuade the panel to roll back national education policy to 1994, when the federal role was much more limited.

Some Democrats argued that the Harkin-Enzi bill is too soft on the states and would not do enough to compel failing schools to improve.

“This is the biggest federal retreat that I think we’ve had in domestic policy that I can remember,” said Sen. Michael F. Bennet (D-Colo.), a former Denver school superintendent. “Children are being shackled to a place where they’re getting no education at all. . . . We’re holding onto one small sliver, children who are marooned, and were saying, ‘You need to do something about it if you take federal funds.’ To insist that the very bottom of the heap be dealt with is not excessive federal intervention.”

When No Child Left Behind was enacted in 2002, it marked an unprecedented reach into education by the federal government, propelled by a bipartisan alliance between President George W. Bush and the late Sen. Edward M. Kennedy (D-Mass.), who argued that states receiving federal money for education must be held accountable for results.

The law was embraced by civil rights groups that believed that struggling children were hidden from view, their test scores obscured by school averages, and that failing schools had no incentive to improve on their own.

But in the nine years since No Child Left Behind was enacted, schools, states and teachers unions have widely complained that its goals are unrealistic and the sanctions draconian.

The law was due for reauthorization four years ago.

Last month, President Obama said he was so frustrated by congressional inaction that he would direct Education Secretary Arne Duncan to waive the requirements of the law for states that embrace education policies favored by the White House. At least 39 states, in addition to the District of Columbia and Puerto Rico, intend to apply for a waiver.

Harkin, Enzi, Alexander and others in the Senate want to pass a bill by the end of the year, before the waivers are issued.

Harkin agreed to hold a hearing on the legislation next month before the bill goes to the Senate floor.