Elaborating, Clark said a president must have judgment, not merely courage and character.
, the Democratic presidential hopeful, said Clark's comments had been inartful. But McCain's campaign judged them worse, and worked to stoke the controversy.
One ally of the Republican presidential contender accused Obama of "winking and nodding" when he should be condemning Clark and his comments. "This is now about Obama, not Wesley Clark," added Orson Swindle on a conference call with reporters organized by the Republican presidential candidate's campaign.
Swindle, a retired colonel and - like McCain - prisoner of war in Vietnam, added that Obama should tell his surrogates to "knock this crap off."
Clark set off the controversy on Sunday when he said McCain's wartime experience as a Navy pilot and his command of an air squadron in peacetime was did not provide him with experience needed to become president.
"I don't think riding in a fighter plane and getting shot down is a qualification to be president," he added at the time.
McCain frequently emphasizes his military service as he campaigns for the White House.
Obama, who did not serve in the military, frequently cites his opposition to the 2003 invasion of Iraq as evidence of the judgment needed in a commander in chief.
Despite criticism from Republicans, Clark declined to back down in a morning interview with ABC on Tuesday. "The experience that he had as a fighter pilot isn't the same as having been at the highest levels of the military and having to make ...life or death decisions about national, strategic issues," he said.
Asked whether he felt he owed McCain an apology, Clark responded, "I'm very sorry that this has distracted from the message of patriotism that Sen. Obama wants to put out."
Later, in a National Public Radio interview, Clark was asked about his statements in 2004 that Sen. John Kerry, the Democratic presidential candidate, had "heard the thump of enemy mortars, He's seen the flash of tracers" and could lead in a time of war.
"I think that you can always cite a candidate's service in the armed forces as a testimony to his character and his courage. But I don't think early service justifies moving away from looking at a candidate's judgment," he replied.
McCain's campaign responded with its second conference call by surrogates on this subject in two days.
Sen. Lindsey Graham, R-S.C., rebutted Clark's claim by arguing that McCain's years as a prisoner of war and the mistreatment he endured made him uniquely qualified to lead the campaign in the Senate to ban the use of torture in the interrogation of detainees in the war on terror.
"Nobody could have taken the floor and spoken about detainee policy" the same way, Graham added.
Obama, campaigning in Ohio, said he did not believe Clark's intent was the same as critics who four years ago challenged John Kerry's account of his own wartime service in Vietnam. The so-called Swift Boat ads are is widely blamed by Democrats for playing a role in Kerry's defeat in the presidential race in 2004.
"I don't think that Gen. Clark had the same intent as the Swift Boat ads of four years ago. I reject that analogy," Obama said.
He said McCain "deserves the utmost honor and respect for his service to our country."
At the same time, he said his admonishment - in a Monday speech on patriotism - against devaluing McCain's military service had been in early drafts of his speech, and was not added at the last minute in response to what Clark had said.
"The question is why, given all the vast numbers of things that we've got to work on, that would be a top priority of mine," he said. "The fact that somebody on a cable show or on a news show, like Gen. Clark, said something that was inartful about John McCain, I don't think is what is keeping Ohioans up at night," he said.
On Monday, Obama campaign spokesman Bill Burton said, "Sen. Obama honors and respects Sen. McCain's service, and of course he rejects yesterday's statement by Gen. Clark."