The best way to end the policy is for the "Senate to follow the lead of the House of Representatives," Gibbs said Wednesday. "This is a policy that is going to end. It's not whether it will end. But the process by which it will."
The House approved a repeal as part of the annual defense budget earlier this year, but the Senate failed to approve the measure in a vote last month.
"I feel strongly this is an action that needs to be taken by the Congress and that it is an action that requires careful preparation, and a lot of training and a lot of revision of regulation," Defense Secretary Robert Gates told reporters on a flight to Brussels Wednesday.
The administration's position has not been well received by many advocates for gay and lesbian rights, who insist a repeal should not be put on hold.
"We had hoped that if President Obama truly believed that 'Don't Ask, Don't Tell' is wrong, particularly because it violates the First and Fifth Amendments, that he would use Judge Phillips' ruling as a means to end the policy," said Christian Berle with the Log Cabin Republicans, a conservative gay rights group.
"It is really confusing and also heartbreaking for these service members who continue to put themselves in harm's way in service to their country," said Michael Cole, spokesman for the Human Rights Campaign. "Instead of the policy being repealed we've gone through seemingly endless legal wrangling and legislative posturing that has not served our national security interests."
The administration has said it is obliged to defend the policy in court, and Obama has said he would prefer it to be repealed legislatively.
"The Justice Department is defending the statute, as it traditionally does when acts of Congress are challenged," said Justice Department spokeswoman Tracy Schmaler in a statement.
The case was brought in 2004 by the Log Cabin Republicans, which argued that the military's 17-year-old policy violates gay service members' rights to free speech, open association and due process. Judge Phillips agreed.
The Log Cabin Republicans estimate that 13,500 gay military service members have been ousted under the rules since 1994.
Phillips' decision marked the first time a federal judge had found the law unconstitutional on the grounds of due process and First Amendment violations.
Seventy-five percent of Americans say gays who disclose their sexual orientation should be allowed to serve in the military, according to a recent ABC News/Washington Post poll, up from 44 percent 17 years ago.