Obama said problems with VA reporting systems "did not surface to the level" where Shinseki or the White House were aware of them.
Obama said there was "a need for a change in culture" at veterans hospitals "and perhaps the VA as a whole" to make sure that problems and "bad news" don't get covered up, but get reported and fixed.
Obama said he would demand accountability if problems were found at VA medical facilities, and accepted Shinseki's resignation. The two met at the White House before the President announced the the development, which came as political pressure mounted for the Cabinet officer to step down.
"I regret he has to resign under these circumstances," Obama said.
Speaking earlier Friday to a veterans group, Shinseki said he underestimated the depth of problems in the VA system and announced several steps, fixes, including removal of senior leaders at the Phoenix VA hospital and elimination of performance awards for VA leaders in 2014.
The retired Army general also apologized to veterans and Congress, but declared: "This situation can be fixed."
He then went to the White House to meet with Obama about the problems that gained prominence after CNN began reporting problems at VA facilities in November. He left the White House after the meeting.
In an interview taped Thursday and broadcast Friday on ABC, Obama promised "a serious conversation" with Shinseki "to see whether he thinks that he is prepared and has the capacity to take on the job of fixing it because I don't want any veteran to not be getting the kind of services they deserve."
A source close to Shinseki said the retired Army general indicated in conversations this week that he will not offer his resignation unless asked for it.
"He's not stubborn, but he will go in armed with the facts. He knows what to do. He knows it's an uphill battle," the source said ahead of Shinseki's meeting with the President.
Facing mounting calls to resign, Shinseki on Friday spoke to representatives of the people particularly vulnerable to his agency's medical failings. He was the featured speaker at the National Coalition for Homeless Veterans' annual conference in Washington.
Shinseki received a standing ovation at the beginning and end of his appearance. After touting improvements in delivery of services to homeless veterans, Shinseki said at the end that he wanted to talk about "the elephant in the room."
The secretary said he was shocked by the inspector general's report, released Wednesday, on failings in the VA system, especially the prevalence of wait lists for veterans needing medical care.
"That breach of integrity is irresponsible, it is indefensible and unacceptable to me," he said. "I said when this situation began weeks to months ago and I thought the problem was limited and isolated because I believed that. I no longer believe that. It is systemic."
Shinseki, who has been VA chief for five years, said he was misled by others.
"I was too trusting of some, and I accepted as accurate reports that I now know to have been misleading with regard to patient wait times," he said. "I can't explain the lack of integrity among some of the leaders of our health care facilities. This is something I rarely encounter during 38 years in uniform and so I will not defend it because it's indefensible, but I can take responsibility for it and I do."
Among other changes announced: eliminating wait times as a way to evaluate supervisors' performance, accelerating administration of care to veterans and asking Congress to fill VA leadership vacancies quickly.
In the latest accusation against the agency, U.S. Reps. Mike Doyle and Tim Murphy of Pennsylvania issued a statement saying 700 veterans had been placed on a primary care waiting list for doctor appointments at the Pittsburgh VA center, with some waiting since 2012.
Late Thursday, a ranking Democratic congressman on the Veterans' Affairs Committee joined colleagues from both sides of the aisle to demand Shinseki throw in the towel.
"Democrats and Republicans alike, in tandem with our Veteran Service Organizations and the millions of Americans who have served our nation, all want to get to the bottom of what exactly is broken with the VA system, and what we can do to fix it," Rep. Mike Michaud of Maine said in a statement.
But Shinseki has become the focal point, and it is time for him to go, so progress can be made, he said.
"The systemic failures in our VA system are inexcusable and must be fixed immediately so that this never happens again," he said.
A number of Democratic senators -- many of them facing rough re-election battles this year -- have joined the bipartisan chorus urging the secretary to resign or the President to fire him.
"The inspector general's preliminary report makes it clear that the systemic problems at the U.S. Department of Veterans Affairs are so entrenched that they require new leadership to be fixed," said Mark Udall of Colorado, the first Senate Democrat to call for a change at the top.
Calls for criminal investigation
Resignation may be just a prelude to the fallout to come.
There have also been calls for a criminal investigation into at times deadly delays in care at Veterans Affairs hospitals.
The President found the report deeply troubling, and a White House official speaking on the condition of anonymity told CNN that Shinseki was on "thin ice" with Obama.
Some lawmakers in Congress were incensed after this week's release of the preliminary inspector general's report that described a "systemic" practice of manipulating appointments and wait lists at the Veterans Affairs Medical Center in Phoenix.
The VA inspector general reported that at least 1,700 military veterans waiting to see a doctor were never scheduled for an appointment or were placed on a waiting list at the Phoenix VA, raising the question of just how many more may have been "forgotten or lost" in the system.
Breaking the scandal
CNN reported exclusively last month that, according to sources, at least 40 American veterans died while waiting to be seen at the Phoenix VA. CNN also obtained an e-mail that an employee at a Wyoming clinic of the VA wrote saying that employees were instructed to "game the system" to make the clinic appear more efficient.
Rep. Steve Israel of New York, the head of the Democratic Congressional Campaign Committee, is among those calling for a criminal investigation by the Department of Justice.
"I want to know if anybody at the VA doctored papers, engaged in a cover-up, withheld care from veterans," he told CNN, adding the demand in the form of a letter was hand delivered Thursday to Attorney General Eric Holder's office.
"They need to be investigated. They need to be prosecuted. They need to be fired."
Republican Rep. Jeff Miller of Florida, chairman of the House Committee on Veterans Affairs, made a similar demand of the Justice Department.
"I think the facts are too many now for them to look the other way," he said.
The Justice Department is reviewing the VA inspector general's report but has not formally opened an investigation, Peter Carr, an agency spokesman, has told CNN.
The VA has acknowledged 23 deaths nationwide due to delayed care. The VA's acting inspector general, Richard Griffin, told a Senate committee in recent weeks that his investigation so far had found a possible 17 deaths of veterans waiting for care in Phoenix.
But he added that there was no evidence excessive waiting was the reason.
Among the findings at the Phoenix VA, investigators determined that one consequence of manipulating appointments for the veterans was understating patient wait times, a factor considered in VA employee bonuses and raises, the report said.
Miller believes the actions may be in part about money for "VA bureaucrats."
"Why else would somebody work so hard to manipulate the lists?" Miller said.
The issue of patient wait times is not an overall performance factor ordered by the VA, Dr. Thomas Lynch, the VA's assistant deputy undersecretary for clinical operations, told Miller's committee.
The factors tied to bonuses and raises are decided by each VA network, Lynch said.
The VA inspector general's report did not offer any further details about financial incentives.
Shinseki says he's 'not waiting'
In an opinion piece published Thursday in USA Today, Shinseki wrote that he's "not waiting to set things straight."
"I immediately directed the Veterans Health Administration ... to contact each of the 1,700 veterans in Phoenix waiting for primary care appointments in order to bring them the care they need and deserve," Shinseki wrote.
Shinseki reiterated other steps he's taken, including ordering a "nationwide audit of all other major VA health care facilities to ensure understanding of, and compliance with, our appointment policy."
Some question whether removing Shinseki would address the core problems at the VA or simply serve as a distraction for now.
"Is him resigning going to get us to the bottom of the problem? Is it going to help us find out what's really going on?" asked House Speaker John Boehner, the chamber's top Republican, adding that his answer so far was "no."
House Democratic Leader Nancy Pelosi also warned against targeting only Shinseki.
She, too, has joined the push for a criminal investigation of the VA problems, saying "certainly what was done was dishonest."