Government lawyers warned U.S. District Judge Virginia A. Phillips not to overstep her bounds while ruling on a lawsuit by the Log Cabin Republicans.
The attorney for the gay rights group argued that the "don't ask, don't tell" policy violates the constitutional rights of gay military members to free speech, due process and open association.
"Log Cabin Republicans have brought this case to trial to call out the government on the wrong it's doing on current and future homosexuals who wish to serve their country," said Attorney Dan Woods. "We ask you to do them right," Woods told Phillips.
The closing arguments came at the end of the two-week trial.
It's not clear when Phillips will hand down a ruling, but legal experts say Phillips may hold off to see if Congress repeals the policy.
In late May, the House voted to repeal the policy. The Senate is expected to act on the issue this summer.
U.S. Department of Justice attorney Paul G. Freeborne said during his closing arguments that Woods was asking the judge to go beyond her powers.
"We do not believe the court has the authority to issue a nationwide injunction," said Freeborne.
Log Cabin Republicans include former and current members of the military. The group says more than 13,500 service members have been fired under the law since 1993.
Testimony from former service members included a decorated Air Force officer who was dismissed after fellow officers snooped through his personal e-mail in Iraq and a sailor whose supervisor concluded he was gay after he refused to visit prostitutes.
Woods argued the military has relaxed its standards and now allows convicted felons to make up for a shortage of personnel while the country is at war.
"In other words, our military will give a convicted felon a gun, but will not give a gay guy a typewriter," said Woods.
AP contributed to this report.