Washington (CNN) Recently fired Veterans Affairs Secretary David Shulkin declined on CNN's "State of the Union" Sunday to offer a full endorsement of Ronny Jackson, President Donald Trump's pick to replace him.

Instead, Shulkin praised Jackson's values.

"The Senate has to make up their own mind," Shulkin said. "And it's important to follow the process, which is to do a proper vetting, and I don't think there should be shortcuts in that. But I do believe that the President needs somebody that he has confidence in to get this job done and somebody that he's got a good rapport with."

Jackson, the White House physician, is facing criticism over his inexperience in managing an institution as large as the VA, which has roughly 370,000 employees.

Pressed by CNN's Jake Tapper on whether he would endorse Jackson, Shulkin again stressed the difficulty of the task at hand for an incoming VA secretary.

"I believe in Dr. Jackson's values," Shulkin said. "I think that's important. I know that he cares a lot about veterans, and I believe that he will work well with the President.

"But this is a big job that has to be thought about carefully."

Trump announced on Wednesday that he was replacing Shulkin with Jackson as his new permanent choice to run the massive department.

'I did not resign'

Shulkin broke with the White House on the circumstances of his ouster during his interview. A White House spokeswoman told Politico in a piece published Saturday that Shulkin "resigned from his position," but in the interview, Shulkin said, "I did not resign."

Citing a statement made last week by White House deputy press secretary Lindsay Walters, claiming that Shulkin resigned from his post, assistant press secretary Ninio Fetalvo replied to CNN in an email Sunday morning: "Our statement still stands."

Shulkin's firing came after an inspector general report took issue with the VA's use of taxpayer funds on Shulkin's travel. For his part, Shulkin has defended his conduct and said people who have ideological disagreements with him used the report as a "political exploit" to remove him from leadership.

Shulkin expanded on comments he made in an op-ed where he blamed political appointees for working against him in the interest of aggressively privatizing the work of the department.

"These individuals, though, when they didn't see that their way was being adopted, used subversive techniques to be able to change leadership at the VA," Shulkin said. "That's the issue that I have concerns with."

Sanders: Removal about privatization

In a separate interview on the same program, Vermont independent Sen. Bernie Sanders said Shulkin's firing was "part of a broader approach of the Trump administration" to tilt the federal government toward the private sector and a conservative course desired by major donors, referencing the Koch brothers in particular.

"What you're looking at under the leadership of the Koch brothers is a massive effort to privatize agencies of the United States government and give them over to private corporations," Sanders said. "That is what the removal of Shulkin is all about."

Sanders, a member of the Senate Veterans Affairs Committee, said he opposed privatization and would oppose a nominee who would not "strengthen" the VA. CNN reached out to Americans for Prosperity, the advocacy group backed by the Koch brothers, for comment.

Dan Caldwell, executive director of the Koch-affiliated group Concerned Veterans For America, said in a statement issued on Monday that Sanders' comments were not surprising, citing a Washington Post fact-check of Democratic critiques of the group, and said their efforts were in line with many others addressing problems at the VA.

"No one wants to diminish the VA's comparative advantage of delivering specialized care like prosthetics and psychiatric counseling. However, veterans deserve the opportunity to access private care when the VA is failing them," the statement read.