Congressional backers of the District’s private school vouchers said Monday that they had struck a deal with the Obama administration to keep money and students flowing into the controversial program.

House Speaker John A. Boehner (R-Ohio) and Sen. Joseph I. Lieberman (I-Conn.), the authors of legislation that reauthorized and expanded the Opportunity Scholarship Program, said they had reached an agreement with the White House to ensure that enrollment in the program can grow and that parents can apply to have their children stay in or join the program and get a response as soon as possible.

“I’m pleased that an agreement has been reached to expand the program, consistent with the law already on the books,” Boehner said, praising the scholarships as “both effective and cost-effective.”

Although many Democrats oppose the scholarship program, President Obama agreed to sign Boehner and Lieberman’s legislation in April of last year as part of a broader budget deal. But supporters of the vouchers have complained that the administration was trying to undermine the program, particularly because Obama did not request any funding for the scholarships in his fiscal 2013 budget. Boehner and others accused the administration of improperly limiting enrollment and diverting leftover money in the program to other purposes.

In a statement Monday, Education Secretary Arne Duncan said the administration and Boehner had agreed to increase “the current enrollment of about 1615 to approximately 1700 students for the coming year to allow for a statistically valid evaluation of the program,” as Congress has mandated that the department conduct such a study.

“The President and I are committed to ensuring that the education of the children currently in the D.C. Opportunity Scholarship program is not disrupted,” Duncan said. “Beyond that commitment, however, we remain convinced that our time and resources are best spent on reforming the public school system to benefit all students and we look forward to working with Congress in a bipartisan manner to advance that goal.”

The program gives low-income District students money to help pay for private school tuition. Many of the scholarship recipients attend the city’s Catholic schools, which have long been a cause close to Boehner’s heart. Under his legislation, the city gets $60 million in federal funds each year, with the money equally divided among traditional public schools, charter schools and the voucher program.

The opportunity scholarships have long divided local leaders. Mayor Vincent C. Gray (D), Del. Eleanor Holmes Norton (D-D.C) and teachers unions oppose the program, arguing that it diverts money and attention from public schools. Former mayors Adrian M. Fenty (D) and Anthony A. Williams (D) and former D.C. Council chairman Kwame R. Brown (D) backed it.