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Defense Secretary Robert Gates said Tuesday that he supports President Obama's decision to seek the repeal of the "Don't Ask, Don't Tell" policy prohibiting gays from serving openly in the military and has appointed a "high-level working group" to figure out how to do it.

Gates, in testimony before the Senate Armed Services Committee, announced that Gen. Carter Ham, who leads U.S. Army forces in Europe, and Pentagon General Counsel Jeh Johnson will lead the review. The defense chief called for an "implementation plan" by the end of the year.

"I fully support the president's decision," Gates said. "The question before us is not whether the military prepares to make this change, but how we ... best prepare for it. We have received our orders from the commander in chief and we are moving out accordingly."

Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, echoed Gates' remarks and added that, in his "personal view," changing the policy is the "right thing to do."

"I cannot escape being troubled by the fact that we have in place a policy that forces young men and women to lie about who they are in order to defend their fellow citizens," Mullen said. "For me, personally, it comes down to integrity -- theirs as individuals and ours as an institution."

Mullen said he believes, but does not know for a fact, that military personnel will "accommodate" a change in the policy.

Obama said during the State of the Union address last week that he will work with Congress "this year" to repeal the controversial policy, renewing a campaign pledge that fell by the wayside last year as the president devoted his energy to health care reform.

But Gates cautioned Tuesday that no matter how much the Pentagon studies the issue, the "ultimate decision" rests with Congress.

A senior Pentagon official earlier told Fox News it does not appear the votes are there in Congress to actually change the law, but said it is not the Pentagon's role to get involved in that aspect.

Sen. John McCain, R-Ariz., ranking Republican on the Armed Services Committee, said Tuesday he was "deeply disappointed" by Gates' remarks and reminded him that the plan requires the support of Congress. He said that the administration should not repeal the policy, which he called "imperfect but effective," at a time when the nation is engaged in two wars.

"Has this policy been ideal? No, it has not. But it has been effective," McCain said.

Mullen and Gates acknowledged that the Pentagon is embarking on the change in policy in war-time but argued that the military could do so thoughtfully and objectively, with minimal disruptions.

Gates said the review, among other things, would examine how a repeal would affect policies on base housing, benefits and other issues.