WASHINGTON — Taxpayer-funded tutoring for poor children is paying off in some city schools, a federal study has found.

Students who received the tutoring under the federal No Child Left Behind law improved on reading and math tests, according to the study conducted by independent researchers for the Department of Education and released last week.

Students in schools that fail to hit academic targets for three years in a row are given free tutoring under the 2002 education law.

The study looked at nine urban school districts: Baltimore; Chicago; Denver; Long Beach, Calif.; Los Angeles; Palm Beach, Fla.; Philadelphia; San Diego; and Washington, all chosen because of their large size.

It found students who received tutoring in five of the districts improved in math and reading. The researchers didn't say which districts.

Researchers found no change in student scores in two districts. The results were set aside in two other districts because not enough students got tutoring there to yield valid results.

The tutoring provisions in the law have been criticized by teachers' unions, which complain that tutors don't have to meet the same licensing requirements as regular teachers. In addition, some school district officials object to the law's requirement that they use up to 20 percent of their federal aid for poor students to pay for tutoring, or for transporting the children out of failing schools.

The cost of tutoring ranges from about $800 to $2,000 per child, depending on the district, according to Nina Rees, who oversaw the implementation of the tutoring provision of the law at the Education Department until last year.

Rees said the study should give a boost to those who advocate allowing tutoring to be offered earlier by failing schools. Currently, the law requires that tutoring be offered after a school has missed its progress goals for three years in a row.

The five-year-old No Child Left Behind law is up for renewal in Congress this year.

The law also allows students in schools missing annual benchmarks to move to another public school.

But the study found that few students are choosing to do that — too few to draw conclusions on how transferring to another school affects a student's academic performance, said Ron Zimmer, a senior policy researcher at the Rand Corporation, which conducted the study.