WASHINGTON, May 18 (Reuters) - White House Chief of Staff Denis McDonough said President Barack Obama is "madder than hell" about possible deadly healthcare delays at the Department of Veterans Affairs and is determined to investigate and fix any flaws in the system.

"We're going to get to the bottom of those things, fix them and ensure that they don't happen again," McDonough said on CBS's "Face the Nation" in an interview aired on Sunday.

The allegations that delays in treatment at veterans hospitals could have led to otherwise preventable deaths has sparked a growing political scandal, including calls for the resignation of VA Secretary Eric Shinseki.

A top department official, Undersecretary of Health Dr. Robert Petzel, resigned on Friday in a move critics said was an effort at damage control. But McDonough sidestepped questions about whether Shinseki had Obama's full confidence.

"The president will continue to demand that he and all of us who work for him continue to fix these things until they are functioning the way that our veterans believe they should," McDonough said.

Petzel's resignation came a day after he appeared alongside Shinseki at a congressional hearing about accusations that VA medical facilities in Phoenix covered up long wait times for patients, including 40 who died while awaiting care.

Dr. Sam Foote, a whistleblower in the VA case, said on "Fox News Sunday" that Petzel's resignation was "a great first step". He said there was no way officials in Washington did not know of the issue.

"They knew this was a big problem," he said, adding he believed Shinseki should stay in his job to keep the focus on fixing the problem.

"I think our best bet at this point is to keep the secretary on board. But I think the president needs to keep him on a pretty short leash," Foote said.

The VA has put three senior officials in Phoenix on administrative leave after doctors there said they were ordered to hold veterans' names for months on a secret waiting list until a spot opened up on an official list that met the agency's two-week waiting time goals.

Allegations have been reported about similar cover-up schemes at VA medical facilities in at least seven other cities. The agency runs the largest U.S. healthcare group, overseeing some 1,700 hospitals, clinics, nursing homes and other facilities. (Reporting by John Whitesides; Editing by Jim Loney)