Veterans Affairs Secretary Eric Shinseki speaks with reporters on Capitol Hill on May 15. (Cliff Owen/AP)

Veterans’ Affairs Secretary Eric K. Shinseki vowed Thursday to stay in office and pledged to address the allegations of health care mismanagement that have besieged his agency and the Obama administration.

In a brief interview with reporters on Capitol Hill, Shinseki initially demurred when asked why he thought he should keep his job. When a reporter noted that he’s been “under the gun” all week, Shinseki quickly shot back: “This is not the first time.”

Shinseki is a former Army general who served two tours of duty in Vietnam and earned a Purple Heart after losing part of his right foot in battle. He was unanimously confirmed as VA secretary on the first day of Obama’s presidency in January 2009.

“I came here to do one thing, which is to take care of veterans and families,” he said. “We’ve run hard for five years; I think we have good things to show for it.”

But VA has come under scrutiny for the level of care it provides, after allegations that some department employees had falsified data to hide the long wait times some veterans had to endure before they could receive treatment. The uproar has produced many calls for Shinseki ‘s resignation, but the secretary said Thursday he had not offered his resignation to President Obama and had no plans to do so.

Members of Congress on both sides of the aisle are now calling for Veterans Affairs Secretary Eric Shinseki’s resignation. PostTV explains the timeline of the VA health-care scandal. (Pamela Kirkland/The Washington Post)

“Every day I come to work, the idea is to make things better for veterans,” he said. “This is Memorial Day weekend and we have a lot to be thankful for, and a lot to remember . . . I happen to be a veteran and I understand what this is about and they deserve our best work. They’re going to get it.”

Shinseki’s declaration came as Democratic Senate candidates began calling for his ouster and House Speaker John A. Boehner (R-Ohio) signaled increased concern about the unfolding scandal. All week Shinseki has faced growing calls for his resignation from Democrats and Republicans as his own office, VA’s inspector general and congressional committees continue to probe whether staffers at some VA facilities had doctored records to cover up lengthy wait times and that some patients had died while waiting for care.

VA officials launched a nationwide audit of facilities this week to review allegations of doctored schedules and delayed medical care for veterans. Shinseki said the review is “about halfway through” and he expects to deliver initial findings to Obama next week. A full review by his office will be completed in June, he said. A separate investigation by VA’s inspector general isn’t expected to be completed until August.

Shinseki visited the Capitol for a 30-minute meeting with Sen. Richard J. Durbin (D-Ill.), who had requested information on allegations involving VA facilities in Illinois and an update on the ongoing audits.

The secretary’s visit came shortly after Boehner said he’s getting “a little closer” to calling for Shinseki’s resignation amid new reports of problems at VA facilities in Ohio.

“This isn’t about the secretary. It’s about the entire system underneath him,” Boehner said. “And you know, the general can leave and we can wait around for months to go through a nomination process and we get a new person. But the disaster continues.”

Meanwhile, the House Veterans’ Affairs Committee threatened to issue subpoenas to three senior VA officials if they fail to appear before the panel by May 30 to answer questions. The officials did not show up Thursday for a hearing in which the panel called them to testify about the department’s efforts to comply with the information requests.

“My patience is wearing very thin,” said committee chairman Jeff Miller (R-Fla.). “I don’t want to break and make this a partisan issue, because it is not a partisan issue.”

Rep. Michael H. Michaud (D-Maine), the committee’s ranking Democrat, agreed. “I think we do have to make the department aware that we do mean business,” he said.

Senators also sparred over whether to quickly approve the VA Accountability Act, a bill the House passed overwhelmingly Wednesday. The measure would make it easier for the VA secretary to demote or fire senior career employees found to be culpable in cases of delayed care or mismanagement.

On Thursday, Sen. Marco Rubio (R-Fla.) sought to hold a vote on the measure before the start of a week-long Senate recess, but Democrats blocked him.

The Senate Appropriations Committee added the language of the bill as an amendment to a spending measure for VA facilities and construction. Lawmakers added $5 million to the VA inspector general’s budget for its ongoing investigation and included language prohibiting bonus payments to employees of the Veterans Health Administration until the investigation is completed.

Two Democratic candidates for U.S. Senate called for Shinseki’s ouster. Kentucky Secretary of State Alison Lundergan Grimes (D), who is running against Senate Minority Leader Mitch McConnell (R-Ky.), and South Dakota Democrat Rick Weiland, who is seeking to replace retiring Sen. Tim Johnson (D-S.D.), both called on the secretary to step down.

McConnell has said that changing top VA leadership “might be a good thing” but hasn’t called for Shinseki to go.

Josh Hicks and Sean Sullivan contributed to this report.