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Despite a new sense of vigor in the candidacy of Mrs. Clinton, who had raised questions about Mr. Obama’s experience to guide and protect the nation, his advisers were planning to unveil a new strategy to persuade Democrats to coalesce around him for the good of the party.

“We know that there’s not going to be a huge shift in delegates one way or the other, just given the math,” Mr. Obama told reporters earlier in the day as he flew across Texas.

That meant, he said, “either way we’ll go on to Mississippi and Wyoming next week.”

Democrats are scheduled to hold caucuses on Saturday in Wyoming. The Mississippi primary is next Tuesday.

For weeks, the Obama campaign has been organizing in both of those states. And Mr. Obama was hoping for a strong showing in them to help replenish the confidence that sustained his campaign throughout February as he racked up victories in all corners of the country.

While Mr. Obama emerged from the four primaries on Tuesday with an advantage in pledged delegates, efforts to persuade Democrats to unite around him were slowed by the strongest performance Mrs. Clinton had registered in a month.

“We are going to have to earn this victory,” he told reporters on Tuesday. “We are running against very determined and tough opponents, and I want to make sure we never forget that.”

A bruising advertising campaign by Mrs. Clinton appeared to have raised fresh concerns about his candidacy. Democratic voters in Ohio who made up their minds in the final days before the primary favored her, according to exit polls.

David Axelrod, the chief strategist for Mr. Obama, said the Clinton campaign had pursued the approach of “attack, attack, attack.” But the defeats in Rhode Island, Ohio and Texas would not greatly affect the state of the race, Mr. Axelrod said, adding, “They promised they would wipe out our delegate lead, but they haven’t put a dent in it.”

Mr. Axelrod signaled a fierce fight in the coming weeks. “What’s good for the goose is good for the gander,” he said.

He said voters should consider Mrs. Clinton’s decision not to release her tax returns and papers from former President Bill Clinton’s library. Mr. Axelrod also challenged the press to look closely at her legislative achievements.

Still, Mr. Obama’s advisers were poring over the trends that emerged Tuesday, particularly with an eye on Pennsylvania, the next major primary.

Mrs. Clinton maintained an edge over Mr. Obama among women, whites, Hispanics, older voters and those with less education. Mr. Obama continued to edge her out among men, blacks, younger voters and those with more education, according to an exit poll conducted statewide by Edison/Mitofsky for the National Election Pool.

In contrast to a recent trend, Mrs. Clinton was running evenly with Mr. Obama among white men.

“No matter what happens tonight,” Mr. Obama told his supporters here, “we have the same delegate lead as we had this morning, and we are on our way to winning this nomination.”

A version of this article appears in print on , on Page A18 of the New York edition with the headline: Obama Seeks to Rally Backers After Clinton Victories. Order Reprints| Today's Paper|Subscribe
Obama Seeks to Rally Backers After Clinton Victories