The Obama administration unveiled a competition Wednesday to spur reform among early-childhood programs and fuel spending at a time when many states are cutting funding for their youngest students.

The next phase of Obama’s Race to the Top program will distribute $500 million among states that plan to expand access to early-learning programs for children from low-income families and establish clear academic goals and strong evaluation systems.

“Investing in early learning is one of the smartest things we can do,” Education Secretary Arne Duncan said in a telephone news conference. The competition is meant to inspire “bold reforms” that address problems of “uneven quality and uneven access,” he said.

Early-learning programs have been tied to lasting academic success, including higher high school and college graduation rates. Still, only 40 percent of 4-year-olds are enrolled in government-funded preschool programs, according to the most recent report by the National Institute for Early Education Research, based in New Jersey.

“Lawmakers are starting to understand you cannot race to the top when children are not at the starting line,” said Marci Young, project director for Pre-K Now, a campaign of the Pew Center on the States. She said the latest investment is a promising sign that early education could become a bigger priority in the reauthorized federal education law.

State budgets fund the lion’s share of subsidized early-education programs. The federal government spends more than $7 billion on Head Start for children from low-income families, but the program covers only a small portion of eligible children. An additional $5 billion in federal money goes to help low-income working parents afford child care.

Duncan also said that states that competed and lost in two earlier rounds of competition for Race to the Top grants can try for a third round. The grants, totaling $200 million, would range from $10 million to $50 million each and would help advance the administration’s reform objectives, including raising academic standards, improving processes for evaluating and retaining teachers, and turning around low-performing schools.

Eligible states include Arizona, California, Colorado, Illinois, Kentucky, Louisiana, Pennsylvania, New Jersey and South Carolina. South Carolina education officials said Wednesday that the state would drop out of the competition. Maryland and the District won grants in the second round worth a combined $325 million. Virginia withdrew in the second round.

In a news release, Duncan said the latest round would “encourage states to continue their courageous work to challenge the status quo and build on the momentum for education reform happening in our classrooms, schools and communities.”