Mr. Thompson, an Obama supporter, is skeptical about that. “To this day,” he said, “I don’t think Barack Obama has any issue with two people of the same gender getting married.”

Now President Obama says his views on same-sex marriage are “evolving,” and as he runs for re-election he is seeking support from gay donors who want to know where he stands.

This week, he will headline a $1,250-a-plate “Gala with the Gay Community” in Manhattan, his first such event as president; on June 29, he will host a Gay Pride reception at the White House. He is doing so at time when the New York Legislature is considering whether to make same-sex marriage legal — a vote that the president will no doubt be asked about while in New York.

The White House would not comment on whether Mr. Obama was ready to endorse same-sex marriage. But one Democratic strategist close to the White House, speaking only on the condition of anonymity, said some senior advisers “are looking at the tactics of how this might be done if the president chose to do it.”