Dole, however, avoided demanding the resignation of VA Secretary Eric ShinsekiEric ShinsekiShulkin confirmed to lead Dept. of Veterans Affairs Dems to Trump: Exclude VA from hiring freeze Dems, GOP battle over pace of Trump confirmations MORE as other Republicans have, saying he should remain until the White House completes its internal probe of the matter.
Dole did, however, find fault with President Obama's handling of the matter.
"I don't want to be critical of the president, but he waited 23 days before he responded, and I think he should have done it sooner," Dole said.
Shinseki's turmoil is particularly agonizing for Dole. The former Kansas senator introduced Shinseki at his confirmation hearings in 2009, where he praised the retired general as a "true American hero."
Dole, himself severely wounded in World War II, has had extensive involvement with veteran issues, chairing a commission under President George W. Bush that addressed the care received by wounded veterans returning from Iraq and Afghanistan.
Dole also had some criticism for Tea Party members of the Republican caucus in Congress in Friday's interview.
"Some of them are so far right they're going to fall out of the Capitol," Dole joked. "I don't know what they contribute if they're against everything."