AUSTIN, Texas — Senator Clinton said tonight she would not sit down with Raul Castro until he implements political reforms in Cuba, but Senator Obama said he favored a meeting without preconditions.

“A presidential visit should not be offered and given without some evidence that it will demonstrate the kind of progress that is in our interest and the interest of the Cuban people,” Mrs. Clinton said in the opening moments of a campaign debate in advance of the March 4 Texas primary.

She mentioned political freedoms and a more open economy as essential in a country that Fidel Castro ruled in a Communist dictatorship for nearly a half-century. Mr. Castro’s brother, Raul, is likely to be named president by parliament on Sunday.

Moments later, though, Mr. Obama said that unlike his presidential rival, he would be willing to meet “without preconditions.”

“Although Senator Clinton is right that there has to be preparation, it’s very important there has to be an agenda and on that agenda would be human rights, releasing political prisoners,” he said.

The two rivals sat next to one another in swivel chairs in a University of Texas auditorium for the 90-minute debate, one in a dwindling number of opportunities for the former first lady to chart a new course in the presidential race.

She has lost 11 straight primaries and caucuses to Mr. Obama — including an overseas competition for support among Americans living aboard — and has fallen behind in the chase for the number of delegates needed to become the presidential nominee.

Mr. Obama’s strong showing has made him the man to beat in a historic struggle between a black man and a white woman, and even some of Mrs. Clinton’s own supporters conceded she needs victories in both Ohio and Texas early next month to preserve her candidacy. Rhode Island and Vermont also vote that day.

Mrs. Clinton and Mr. Obama articulated well-worn campaign themes in the opening moments of the encounter, she stressing years of experience, and he underscoring a need for a change in the way business is done in Washington.

“I offer a lifetime of experience and proven results,” she said, adding that “if we work together, if we take on the special interests,” the lives of middle-class Americans would improve.

Mr. Obama, too, scorned the power of special interests. “The problem we have is that Washington has become a place where good ideas go to die….They go to die in Washington because too many politicians are interested in scoring political differences rather than bridging differences get things done.”

The Democrats have had at least 18 debates and forums of the campaign, a series that has ranged from highly civilized to hotly confrontational.

The last time the two met, in Los Angeles, they sat side by side and disagreed politely. But in an earlier encounter last month, in Myrtle Beach, S.C., each accused the other of repeatedly and deliberately distorting the truth for political gain in a highly personal, finger-wagging showdown.

In The Associated Press’ delegate count today, Mr. Obama had 1,358.5 to 1,264 for Mrs. Clinton. It takes 2,025 delegates to claim the nomination at this summer’s convention.

In a further sign of his growing strength, Mr. Obama won the endorsement during the day of the Change to Win labor federation, which claims 6 million members. The Teamsters union announced its support for Mr. Obama on Wednesday.

The debate was sponsored by CNN, Univision, and the Texas Democratic Party.