WASHINGTON — Sen. Barack Obama began trying to rally the Democratic Party around him on Thursday. He struck a tougher tone against Sen. John McCain, saying McCain was "losing his bearings" in his pursuit of the presidency.

Even as Sen. Hillary Rodham Clinton persisted with her campaign for the Democratic presidential nomination, Obama made a celebratory return to the Capitol, where he received an enthusiastic reception on the floor of the House in an appearance staged to position him as the party's inevitable nominee.

Behind the scenes, there were new discussions between Obama and the party leadership. Senior Democratic officials said he met with Speaker Nancy Pelosi on Thursday when their paths crossed at Democratic Party headquarters. They had spoken by telephone about the state of the race earlier in the week. The officials declined to discuss the substance of the conversations. Pelosi and Clinton have had no known recent talks.

Addressing concern among some Democrats that Clinton would fight on to the national convention in late August, Terry McAuliffe, chairman of the Clinton campaign, suggested that the race would end quickly after the final primaries in early June, sparing the party a potentially debilitating summer-long battle.

"After June 3, this is going to come to a conclusion," McAuliffe said on NBC's "Today" program.

Other close Clinton allies said much the same thing, evidence of a growing consensus that Clinton has another four weeks to make her case to voters and superdelegates but then should exit quickly if she has not somehow turned the race around. The Clinton campaign continued to grapple with a number of impediments to fighting on, including a decline in fundraising.

"I think she should complete the primary season, and then she has to re-evaluate and her supporters have to re-evaluate," said Rep. Nita M. Lowey of New York, a Clinton backer.

Obama made no public effort to pressure Clinton from the race, and in interviews with CNN and NBC News, he praised her as a formidable candidate who could not yet be counted out. But he said that he was likely to lock up a majority of the pledged delegates — those awarded by voting in the primary and caucus states — after the Kentucky and Oregon primaries on May 20, and that at that point he could declare victory.

While he was respectful to Clinton, Obama seemed eager to challenge McCain. Asked on CNN about McCain's recent statement that the radical Palestinian party Hamas, considered by the United States to be a terrorist organization, would favor Obama's election, Obama said it was offensive and called it a smear.

"And so for him to toss out comments like that I think is an example of him losing his bearings as he pursues this nomination," Obama said.

In the meantime, Obama continued to scoop up more support from the superdelegates, the elected Democrats and party officials whose votes will be necessary for either candidate to secure the nomination.

Reps. Brad Miller of North Carolina and Rick Larsen of Washington said Thursday that they would back Obama. Several more uncommitted superdelegates in Congress told Obama that they would be announcing their support in the coming days, campaign advisers and House Democratic officials said, continuing a months-long pattern in which Obama has won the backing of party insiders at a much greater rate than has Clinton.

Obama's very public arrival in the House chamber on Thursday morning underscored the fact that the most important front in the Democratic nominating fight was suddenly Washington, where many of the superdelegates were milling around on the House floor voting on amendments to a housing bill.

And it was in marked contrast to Clinton's private meetings near the Capitol the day before as she sought to convert undecided lawmakers. Aides to Obama said they saw his visit as an opportunity to create an image of Obama as the soon-to-be-nominee.

"Obviously, people have been anxious about some of the sense of division in the party, and I just wanted to assure them that whatever happens, we will be coming together," Obama told reporters by way of explaining his visit as he made his way through cheering throngs of tourists in the Capitol Rotunda.

In a quest to win over uncommitted superdelegates, Obama is initially going after Democrats who represent districts where he won — or fared well — in a primary or caucus earlier this year. Before trying to convert Clinton's supporters, the Obama campaign is pursuing the few dozen remaining unaligned Democratic officials.

Obama's top aides have also issued a directive to treat Clinton — and her supporters — with respect and make clear that the decision to remain in the race is up to her."

Pelosi's brief meeting with Obama at the national party offices apparently was coincidental, since she was making some political calls in the building while he was meeting with superdelegates.

Pelosi is potentially pivotal in the nomination fight, given her influence over lawmakers and her role as chairwoman of the convention. She has maintained a public neutrality in the race, saying her first priority is to hold or add to her majority in the House.