WASHINGTON — Just one day after the Department of Defense sent surveys to 400,000 members of the armed forces asking for their personal assessments of the military’s ban on homosexuals, an advocacy group committed to overturning the law is urging gay servicemembers not to complete the questionnaire.

The Servicemembers Legal Defense Network said in a statement released Thursday that “while the surveys are apparently designed to protect the individual’s privacy, there is no guarantee of privacy and DOD has not agreed to provide immunity to service members whose privacy may be inadvertently violated.”

The questions, which ask soldiers to judge if issues such as unit cohesion, recruiting, retention and family support would be affected if the law was overturned, will be completed online over a secure connection, according to military officials.

Secretary of Defense Robert Gates responded to concerns about the survey during a press briefing at the Pentagon Thursday.

“I strongly encourage gays and lesbians who are in the military to fill out these forms,” Gates said. “We organized this in a way to protect their privacy and the confidentiality of their responses through a third party, and it’s important that we hear from them as well as everybody else.”

Secretary Gates and Chairman of the Joint Chiefs of Staff, Admiral Mike Mullen, have said publicly they feel it’s time for the law to be overturned. In February of this year Admiral Mullen told Congress, with Gates at his side, he believes it’s “the right thing to do.”

The roughly 90-question survey is part of the Pentagon’s comprehensive review of the “Don’t Ask Don’t Tell” policy that Secretary Gates ordered to be completed by December 2010. He asked that Congress wait to put the matter to a vote until the review is complete, but legislation to repeal the ban has already been inserted into a defense spending bill that could be voted on as early as this month.