Correction: Earlier versions of this article, including Friday’s print edition of The Washington Post, misstated the amount of the grant administered by the District’s Office of the State Superintendent of Education.

In the second year of Race to the Top, the Obama administration’s signature effort to improve public schools, nine of 12 jurisdictions that received $4 billion in federal grants made good progress. But three — the District, Maryland and Georgia — have stumbled, federal officials said.

“We have a lot of good news in this report and also some challenges,” Education Secretary Arne Duncan told reporters Thursday.

The Education Department has been closely tracking the performance of the 12 states, praising those that are performing well while identifying others where problems have arisen.

None of the grantees have been ordered to return federal funds, although Georgia has been moved into a “high risk” category.

To win the money, each state and the District crafted its own plan to improve education from kindergarten through 12th grade. All pledged to implement new systems to evaluate teachers, use data to measure how well students are learning, pump new resources into troubled schools and allow or encourage public charter schools.

The states are now in the third year of the four-year grant. The report released Thursday examined progress made in the past school year.

Federal officials said the District’s greatest failure was that it moved to improve only one of 13 low-performing schools that it had committed to turn around under the terms of the grant.

In addition, the Office of the State Superintendent of Education — which is responsible for administering the $75 million federal grant — was 10 months late in releasing a Web site and other resources meant to help teachers transition to a new set of rigorous national standards, known as the Common Core.

District officials also are months delayed in completing a database meant to track students’ progress throughout their academic careers in D.C. schools.

Federal officials pointed to substantial turnover among staff at OSSE as one reason for the delays. Turnover also was blamed for the District’s failure to meet expectations after the first year of Race to the Top.

The federal government is committed to helping the District, but the city must get moving, Duncan said: “We need all states to show results, and the slow pace of D.C.’s progress needs to dramatically accelerate.”

The Office of the State Superintendent of Education was created in June 2007, when D.C. schools came under mayoral control. The office has had troubles since the outset, facing several structural challenges. It serves as a state education agency in a jurisdiction that is not a state, and it deals with a school system with a chancellor who is the city’s dominant educational figure amid a growing number of public charter schools that are separate school districts in the eyes of the law.

We have been and are currently working to address the problems that were presented,” said Ayan Islam, an OSSE spokeswoman.

Maryland, which won $250 million, has had difficulties hiring qualified staff to run data systems aimed at improving instruction, a key part of its Race to the Top program. And the state had problems developing a new teacher-evaluation system. Officials failed to collect information when new evaluations were piloted last spring, a problem that federal officials attributed to a lack of leadership in Annapolis.

Much of the sputtering occurred during a year-long period when Maryland’s education department was without a permanent superintendent. Lillian M. Lowery assumed the post in July.

“Maryland has had some leadership challenges that the new chief will have to make up, but we have tremendous confidence in her,” Duncan said.

In a statement, Lowery said Maryland is moving ahead. “We have made further strides since this report was completed,” she said, noting that test scores are starting to reflect the impact of the federal grant money. Of the 16 low-performing schools that Maryland is working to turn around, all have met state goals in math and 12 have met state reading goals, Lowery said.

While 22 of Maryland’s 24 school districts are participating in Race to the Top, Montgomery and Frederick counties are not. Leaders in those counties disagreed with the idea of using students’ state test scores as a measure of teacher quality.