The White House said Friday it is proposing a 13.6 percent increase in funding for the handling of veterans benefits, an effort to reduce the Veterans Affairs Department’s massive backlog of disability claims.

The proposed $2.5 billion for the Veterans Benefits Administration is part of an overall 4 percent increase the Obama administration is seeking in the VA’s discretionary budget, an amount that is probably higher than most federal departments and agencies will see when the proposed 2014 budget is released next week.

“The president has made clear to us this is a national priority,” White House Chief of Staff Denis McDonough said at a briefing with VA Secretary Eric K. Shinseki held to draw attention to the administration’s efforts to cope with the backlog.

The number of pending claims filed by veterans seeking compensation stood this month at 885,000,70 percent of which have been pending for more than 125 days. Veterans can wait a year or more for a decision at particularly overloaded regional offices, among them Baltimore.

The backlog has drawn public attention in recent weeks, including a much-discussed call from Time magazine columnist Joe Klein for Shinseki to resign.

Shinseki, 70, a former Army chief of staff who lost a foot to a landmine as a young officer in Vietnam, appeared unruffled by the attacks.

“I hear the criticism out there,” Shinseki said during the briefing. “You make tough decisions, and you deal with it.”

Shinseki acknowledged that the VA has already seen large increases in its funding — 41 percent during the Obama administration — even as the backlog, which stood at 391,000 when the president took office in January 2009, has skyrocketed.

Beyond the number of veterans returning from Iraq and Afghanistan, major reasons for the growth in the backlog include Shinseki’s decisions to ease rules for making claims related to post-traumatic stress disorder and the toxic herbicide Agent Orange.

The Agent Orange decision, which added 260,000 Vietnam-era cases to the system, represented “unfinished business that we wanted to pay attention to,” Shinseki said.

“You have to make those decisions,” he added. “Now you have to come up with a solution.”

Shinseki’s proposed fix includes a paperless claim system now being introduced, one of several changes the VA says will enable it to meet its ambitious pledge to eliminate the backlog by 2015, with all claims processed within 125 days at a 98 percent accuracy rate.

“Our commitment is to end it,” Shinseki reiterated Friday.

The 2014 White House budget request includes $155 million to implement the paperless system, as well as $136 million to convert existing paper records into digital format.

“In a budget that’s taking pretty significant hits, we thought it very important to highlight . . . these investments,” McDonough said.

Major veterans organizations, including the Veterans of Foreign Wars and the American Legion, are skeptical about the VA’s progress toward ending the backlog. But in the wake of Klein’s column, several groups have expressed strong support for Shinseki.

“This guy is a class act, and most veterans appreciate it,” said Bob Hamilton, executive director of the VFW.

Friday’s event appeared aimed at showing continued administration support for Shinseki, whom McDonough said “the president relies on and leans on daily.” But it also underscored a sense of urgency within the White House to reduce the backlog.

“We’re spending an awful lot of time” on the issue, McDonough said.

“Nobody is going to be more impatient about this than the guy we’re reporting to on a regular basis . . . the president,” he added.

The administration’s proposed 2014 budget includes $7 billion for the VA’s mental health-care services, a 7.2 percent increase that the administration says will allow the department to expand treatment for PTSD and sexual trauma.

The budget also proposes to make permanent several tax credits signed into law in 2011 that provide incentives for businesses that hire unemployed veterans.

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