WASHINGTON — The Veterans Affairs Department is chipping away at a massive inventory of disability claims for veterans, reducing the number of claims considered backlogged by about 15 percent in recent weeks.

Republican lawmakers are skeptical that the trend will continue, but they’ve been unable to agree on a solution to a problem that has become a major headache for the Obama administration.

The VA pays disability benefits to veterans who are injured or become ill as a result of their active service. For years, veterans have complained that it takes too long for their claims to be resolved. In late March, more than 633,000 claims, or about 70 percent, were pending longer than 125 days.

But in recent months, the department has taken steps to try to deal with the backlog. The oldest claims in the system were moved to the front of the line and claims processors were required to work at least 20 hours of overtime each month. That has helped to reduce the backlog to just over 531,000, the VA said Thursday.

Among the claims cleared were about 65,000 cases that had been pending for longer than two years. About 2,000 such cases remain.

VA spokesman Josh Taylor said long-term changes, including moving to a new computer system, also have had an impact.

Although the progress appears to have bought the department some time on Capitol Hill, lawmakers still are looking for a long-term solution to the backlog issue.

Rep. Jeff Miller, the Republican chairman of the House Committee on Veterans’ Affairs, reiterated his calls for an independent commission to examine the root causes of the problem and more direct involvement from President Barack Obama.

“If we can’t bring collectively all the people to the table to help resolve it, I don’t see a solution out there,” Miller said Thursday at an event sponsored by Concerned Veterans for America, a political advocacy group.

But Sen. Richard Burr, the ranking Republican on the Senate Committee on Veterans’ Affairs, said he views commissions as a tool to provide the VA with more time.