The primary rivals ran into each other backstage at a hall where both spoke to Jewish leaders, but Obama said there was no mention of how or when she would formally end her long campaign to become the United States' first female president.
Obama showed no impatience, merely smiling and accepting congratulations from colleagues in both parties as he returned to the Capitol for a Senate vote. But other Democrats urged her to get out of the way.
"I don't see why we don't get on with it and endorse" Obama, said Rep. Charles Rangel, a congressman from Clinton's home state of New York. He said it was only a matter of time before he and other Clinton supporters formally back Obama.
Senate Majority Whip Dick Durbin, an Obama supporter, said Clinton's non-concession "creates a pretty delicate situation here, an awkward situation."
"I don't want to push her. Nobody is going to push her," Durbin said on MSNBC. "But the sooner she does, I think the more likely we're going to be organized and ready to win in November."
Obama began focusing on who will join his ticket in the fall. His campaign said the vetting of potential running mates was to be managed by a three-person team of Caroline Kennedy, former Deputy Attorney General Eric Holder and longtime Washington insider Jim Johnson.
Clinton has told lawmakers privately that she would be interested in the vice presidential nomination. Obama was noncommittal after his chat with her behind the scenes at the American Israel Public Affairs Committee.
