WASHINGTON  The Obama administration, fresh off a victory in persuading federal judges to dismiss a torture case for fear of revealing state secrets, is divided over using similar tactics to try to block a lawsuit over government efforts to kill an American citizen accused of ties to Al Qaeda.

The administration’s legal team is debating how aggressive it should be in a brief responding to the lawsuit, which is due Sept. 24. The suit, filed last month, seeks an injunction that would prevent the targeted killing of Anwar al-Awlaki, a radical Muslim cleric who is accused of playing a leading role for Al Qaeda’s branch in Yemen.

Justice Department lawyers are circulating a draft brief with several potential arguments for dismissing the case, and lawyers from national security agencies have met to discuss what should go into the final version. But they have not reached a consensus, according to officials familiar with the discussions, because the arguments seen as strongest also carry significant political and legal risks.

“There are a lot of cross-cutting things going on here, and they have to be very careful about how they litigate this,” said Jack Goldsmith, who was a senior Justice Department lawyer in the Bush administration. “It’s not just a question of winning the case. There is the public diplomacy side, and there are implications for everything else they are doing in the war on terrorism: detention and targeting and other things, too, I imagine.”