WASHINGTON — After months of saying his position on same-sex marriage is “evolving,” President Obama traded that language on Wednesday for comments that stopped just short of endorsing the notion that gay people have the right to marry.

But if his personal evolution is complete, Mr. Obama, who has previously opposed same-sex marriage, is not saying so.

“I think what you’re seeing is a profound recognition on the part of the American people that gays and lesbians and transgender persons are our brothers, our sisters, our children, our cousins, our friends, our co-workers, and that they’ve got to be treated like every other American,” Mr. Obama said at a news conference. “And I think that principle will win out.”

The president went on: “I think we’re moving in a direction of greater equality and — and I think that’s a good thing.”