WASHINGTON — Veterans Affairs Secretary Eric Shinseki maintains his agency is making headway in disposing of more than a half million backlogged disability claims, but a key Republican asserts progress isn’t coming fast enough and is prevailing on President Obama to take direct action.

Senate Republican Leader Mitch McConnell, of Kentucky, told a veterans group recently that the backlog is a “national disgrace” and that it behooves the president to hold the VA accountable for the disarray.

“An issue this important demands attention from the very top,” McConnell said during a presentation before the Veterans of Foreign Wars National Convention. “Veterans ought to be able to count on their government, and they ought to be able to count on their commander-in-chief.”

McConnell maintained that almost 750,000 veterans are affected by the backlog and that more than 60 percent of those have been forced to wait in excess of four months to get a response to their applications.

The situation exists, McConnell noted, despite promises from Obama during the 2008 presidential campaign to reduce the backlog. Efforts to modernize the VA’s claims system and a 40-percent increase in the agency’s budget have failed to produce the desired results.

But the agency countered on Aug. 19 that steps taken by Shinseki have resulted in a 20 percent drop in the in backlogged claims over a four-month period beginning in May, leading the secretary to insist that the agency is “on track to eliminate the backlog in 2015” as promised.

The VA considers a claim to be backlogged when it has been pending for more than 125 days. As of Aug. 14, according to the agency, the backlog stood at 490,000 claims out of 773,000 total claims pending. That’s down from a high of about 608,000 — smaller than the number claimed by McConnell  but four times higher than it was in late 2009 when backlogged claims numbered about 150,000.

Sen. Bernie Sanders, I-VT, chairman of the Senate Veterans’ Affairs Committee, characterized the backlog as “unacceptable” but added that the report of progress in reducing the numbers is welcomed.

“No veteran should have to wait years to receive the benefits they have earned,” Sanders said. “We must remain aggressive and we intend to closely monitor the situation to ensure that the progress continues.”