For complete coverage of Afghanistan, go to the Afghanistan Crossroads blog.

Washington (CNN) -- Gen. David Petraeus told CNN on Thursday that he supports President Barack Obama's July 2011 deadline to start withdrawing U.S. troops from Afghanistan, a key point of contention between the president and many of his Republican critics in Congress.

Petraeus -- tapped to replace Gen. Stanley McChrystal as the U.S. commander in Afghanistan -- expressed his respect and appreciation for McChrystal's work and said the circumstances surrounding the change in command are "sad."

Obama relieved McChrystal of his duties Wednesday after the general and his staff were quoted in a Rolling Stone magazine article making comments that appear to mock top administration officials.

Defense Secretary Robert Gates and Joint Chiefs Chairman Adm. Mike Mullen endorsed Obama's decision during a Pentagon news conference Thursday. Mullen said he was nearly physically "sick" when he read the Rolling Stone story. The comments in the article constituted an unacceptable challenge to civilian authority, the men said.

"We do not have the right, nor should we ever assume the prerogative to cast doubt upon the ability or mock the motives of our civilian leaders, elected or appointed," Mullen said. "We are and must remain a neutral instrument of the state."

Petraeus' remarks to CNN's Dana Bash and Ted Barrett were his first public comments since being chosen as the new U.S. military chief for the Afghan conflict. The Senate Armed Services Committee is set to begin his confirmation hearings Tuesday morning.

"I support the president's policy, and I will also provide the best professional military advice as we conduct assessments," Petraeus said.

The general said it's a privilege to serve. "It's obviously a hugely important mission," he said.

"It's very sad that I have to assume it in this manner," he said. We "all have enormous respect and gratitude to Gen. McChrystal for all that he did. He's played a key role in helping get the inputs right in Afghanistan."

Petraeus declined to immediately say whether he would fire the unnamed officers on McChrystal's staff who are quoted in Rolling Stone making disparaging remarks.

"You have to understand an officer -- a commander -- cannot prejudge a situation because that crosses the line into what is called 'command influence,'" he said. "So we'll need to sort out the facts and take the appropriate action once we've done that."

Mullen emphasized that Petraeus will have the authority to make changes to McChrystal's battle plans and tactics. Obama also reinforced the notion of both tactical and strategic flexibility at the top levels of U.S. command, stressing Thursday that the July 2011 date is only for the start of the process under which U.S. forces will be removed from Afghanistan.

The decision to replace McChrystal with Petraeus was hotly debated by top administration officials. While Gates and Mullen both publicly defended Obama's decision to remove McChrystal, Gates initially backed keeping McChrystal on the job because top Pentagon brass considered the general vital to the Afghan war effort, a senior Pentagon official told CNN's Barbara Starr.

But in a 35-minute meeting in the Oval Office on Tuesday, Obama said he wanted to replace McChrystal with Petraeus, Gates said.

"It was the president's idea," Gates told reporters Thursday. "It was the president who first raised Petraeus' name."

The appointment of Petraeus is the "best possible outcome to an awful situation," Gates said.

Military officers both in Washington and on the ground in Afghanistan have continually stressed Obama's assertion that the switch in leadership does not represent a change in policy.

"Nothing changes about our strategy," said Mullen, who is departing for Afghanistan and Pakistan on Thursday night.

"We remain absolutely focused on our tasks and the operational tempo will not miss a beat," Lt. Gen. Sir Nick Parker said Thursday. Parker, who is British, has assumed command pending Petraeus' confirmation by the U.S. Senate.

Petraeus, who also led the U.S. military surge in Iraq, expressed gratitude toward his wife Thursday, saying he had asked about her feelings on his new assignment

"She's a great wife, army daughter and army mother," he said.

CNN's Ted Barrett, Dana Bash, Barbara Starr and Alan Silverleib contributed to this report.