Speaking after a meeting with Veterans Affairs (VA) Secretary Eric Shinseki, Obama told reporters he would not tolerate any evidence of malpractice.
"When I hear allegations of misconduct ...Whether it's allegations of VA staff covering up long wait times or cooking the books, I will not stand for it," Obama said.
"So if these allegations prove to be true, it is dishonorable, it is disgraceful, and I will not tolerate it -- period."
As many as 40 patients were reported to have died while waiting to be seen by a VA doctor.
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Shinseki, a retired general and Vietnam War veteran, has faced mounting calls to resign and was subjected to a severe grilling by furious lawmakers in Congress last week.
Obama pleaded for patience as the probe into the allegations was carried out.
"I know that people are angry and want a swift reckoning," he said. "But we have to let the investigators do their job and get to the bottom of what happened.
Obama has assigned a close aide, Deputy Chief of Staff Rob Nabors, to investigate the allegations.
Nabors attended today's meeting with Obama and Shinseki, who has held the VA post since 2009.
Asked by reporters if Shinseki had offered to resign, Obama said that the VA chief "was committed to solving the problem and working with us to do it."
"I know that Ric's attitude is if he does not think he can do a good job on this and if he thinks he has let our veterans down, then I'm sure that he is not going to be interested in continuing to serve," Obama said.