President Barack Obama is "madder than hell" about the scandal enveloping the Department of Veterans Affairs, White House chief of staff Denis McDonough said on Sunday.

McDonough spoke two days after Dr Robert Petzel, the under-secretary for health, resigned amid a widening investigation into record falsification and allegations that at least 40 veterans died while waiting for appointments at a VA hospital in Phoenix.

Dr Sam Foote, a whistleblower in the case, said on Sunday Petzel's resignation was "a great first step".

The Dayton Daily News reported that since 2001 the VA has paid out $36.4m to settle claims of “delay in treatment”. The newspaper found 167 cases where delay in treatment was cited as a key reason for the settlement.

“The president is madder than hell,” McDonough told CBS's Face the Nation. “And I’ve got the scars to prove it, given the briefings I’ve given the president.

“Nobody is more outraged about these allegations than the president of the United States.”

On the same talk show Dan Dellinger, head of the American Legion, said it was “unforgivable” that the VA had been hiding delays and called again for the veterans affairs secretary, Eric Shinseki, to resign.

“The issue is we are having veterans die waiting for the care they have earned,” Dellinger said, before calling on Obama to speak out. “We need the White House to come forward,” he said.

At a stormy Senate hearing this week, Shinseki refused to step down. He too said he was “mad as hell” about the allegations of fatal delays and cover-ups. Critics pointed to a 14-day limit to provide care for veterans applying for the first time that was introduced by Shinseki, and said the system was unworkable and resulted in VA administrators devising ways to cover up months-long delays.

“No one should be treated this way in a country as great as ours,” the Arizona Republican John McCain told Shinseki.

“The standard practice at the VA seems to be to hide the truth in order to look good,” said the Washington Democrat Patty Murray. “That has got to change once and for all.”

Critics also rounded on Shinseki’s impassive testimony at the hearing.

“We don’t score testimony on Capitol Hill or otherwise,” said McDonough. “What we score is results to the services and benefits that our vets have earned.

“The president’s demanding that we get to the bottom of the exact allegations that you're talking about as it relates to whether veterans are getting the timely access to care that they have earned.”

On Sunday, Dr Foote told Fox News 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,” he said. “But I think the president needs to keep him on a pretty short leash.”

The VA medical system conducts more than 230,000 appointments every day and is the country’s largest. More than 10 million veterans are covered by the system, which has come under increasing strain from an ageing population and the admission of 2 million new patients since 2009, thanks to the Iraq and Afghanistan wars.

“The buck has got to stop at the top,” said Dellinger. “If this was the military you would be relieved of duty.”

Obama has appointed a key aide to investigate the debacle. Last week, White House deputy chief of staff Rob Nabors was assigned to the VA to work on a review of policies for patient safety rules and the scheduling of appointments.

"While we get to the bottom of what happened in Phoenix, it's clear the VA needs to do more to ensure quality care for our veterans," Obama said in a statement.

On Saturday, McCain blasted Obama for failing to take more action.

“It’s been more than a month since allegations that some 40 veterans died while waiting for care at the Phoenix VA were first made public,” he said, in the weekly Republican address. “To date, the Obama administration has failed to respond in an effective manner.

“Since those initial reports, however, the scandal has gone nationwide, as similar allegations have come to light involving VA clinics and hospitals across America … clearly, the VA is suffering from a systemic, cultural problem that Congress cannot resolve with piecemeal responses. What’s needed is a total refocusing of the VA on its core mission of serving veterans.”