WASHINGTON — Veterans Affairs Secretary Eric Shinseki resigned this morning in a personal meeting with President Barack Obama, shortly after publicly apologizing for deep problems plaguing the agency’s health care system that Obama called “totally unacceptable.”

Obama said he accepted the retired four-star general’s resignation “with considerable regret” during the Oval Office meeting.

Shinseki had been facing mounting calls to step down from lawmakers in both parties since a scathing internal report out Wednesday found broad and deep-seated problems in the sprawling health care system, which provides medical care to about 6.5 million veterans annually.

Obama said Shinseki had served with honor, but the secretary told him the agency needs new leadership and he doesn’t want to be a distraction.

“I agree. We don’t have time for distractions. We need to fix the problem,” Obama said.

The president named Sloan D. Gibson, currently the deputy VA secretary, to run the department on an interim basis while he searches for another secretary. The president said he met with Gibson after accepting the resignation from Shinseki, who has overseen the VA since the start of Obama’s presidency.