Sen. Carl Levin (D-Mich.) predicted Sunday that "Don't ask, don't tell" will be repealed as President Barack Obama promised Saturday.

“I will end ‘Don’t ask, don’t tell,'" Obama said Saturday night at a Human Rights Campaign dinner, without giving a timetable to end the ban on gays serving openly in the military.

"I think he will and he can," Levin said when asked by "Meet the Press" host David Gregory whether the president, who has been criticized by many in the gay community for lagging on gay-rights issues, will follow through on his pledge.

The Senate Armed Services Committee chairman said the policy would have to be changed with "thoughfulness and care," though, and with the input of military leaders.

Former Chairman of the Joint Chiefs of Staff Gen. Richard Myers, also appearing on "Meet the Press," would not weigh in on whether the policy should be overturned, but stressed that the Pentagon and senior military officials must be part of the process.

Former Souther Commander Gen. Barry McCaffrey said it should be up to Congress to change the law.

Armed Services Committee member Sen. Lindsey Graham (R-S.C.) echoed the call for the military to be involved in the process, but likewise didn't weigh in on overturning the policy.

"I'm not going to make policy based on a campaign rally," Graham said.