The government's court filing came two days after U.S. District Judge Virginia Phillips in California ordered the Pentagon to cease enforcement of the law approved by Congress in 1993.
Allowing Phillips' ruling to go forward immediately "will irreparably harm the public interest in a strong and effective military," the government's court papers stated.
Repeated and sudden changes in policy regarding "don't ask, don't tell" will be "enormously disruptive and time-consuming, particularly at a time when this nation is involved in combat operations overseas," the papers said.
The government asked Phillips to respond by Monday "given the urgency and gravity of the issues."
If turned down by the judge, the Justice Department said it would seek a ruling blocking the judge's decision from the 9th U.S. Circuit Court of Appeals in San Francisco.
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However the judge responds, the ban's days are numbered, opponents said. And President Barack Obama agreed.If Phillips agrees to suspend her ruling, "justice will be delayed, but it will not be denied," said Christian Berle, deputy executive director of Log Cabin Republicans, the group that sued and won the ruling overturning the government's policy.
Berle urged Senate Majority Leader Harry Reid "to do what it takes in the lame duck session (after the Nov. 2 election) to end 'don't ask, don't tell' legislatively."
Obama, speaking to a televised meeting of young adults, noted that he, too, is asking Congress to repeal the law, and he said the policy "will end on my watch."
Julie Watson reported from San Diego, Calif.