When it comes to courting Mayor Bloomberg’s endorsement, Senator Obama isn’t leaving much to chance.

The Democratic presidential contender had a plateful of praise yesterday morning for Mr. Bloomberg, the man he asked to introduce him at his economic speech at Cooper Union.

“At a time when Washington is divided in old ideological battles, he shows us what can be achieved when we bring people together to seek pragmatic solutions,” Mr. Obama said at the outset of his address, after thanking the mayor for his “extraordinary leadership.” “Not only has he been a remarkable leader for New York, he has established himself as a major voice in our national debate on issues like renewing our economy, educating our children, and seeking energy independence.”

“Mr. Mayor,” the Illinois senator added, in what approached a public plea for his support, “I share your determination to bring this country together to finally make progress for the American people.”

Mr. Bloomberg was considerably more guarded in his introduction, thanking Mr. Obama for choosing New York as the location for his speech but offering few words that could be mistaken for an endorsement.

“I have not endorsed a candidate for president, but have been very clear in my hope that all the candidates will explain in detail how they will address the great challenges in our country,” the mayor said.

Of Mr. Obama’s speech on the economy, he said: “I’m not sure that everyone of us will agree with every idea, myself included.” A City Hall spokesman, Stu Loeser, said after the speech that Mr. Bloomberg “agreed with a lot of what he heard,” including Mr. Obama’s call for helping people stay in their homes and his proposal to streamline financial regulators.

The two men shook hands warmly as Mr. Bloomberg left the podium, and after the mayor mentioned that Mr. Obama picked up the tab when they met for breakfast in November, Mr. Obama quipped that he expected the favor to be returned.

“The reason I bought breakfast is because I expect payback of something more expensive,” Mr. Obama said, as the crowd laughed. “I’m no dummy,” he joked, in an apparent reference to the mayor’s considerable wealth. He added that while the mayor was a “cheap date,” he had taken note of New York’s plethora of steak houses. Mr. Obama called Mr. Bloomberg yesterday to ask him to introduce him this morning and to review his speech, aides said. Mr. Loeser noted that the senator’s call interrupted the mayor’s meeting with Senator Hagel. Many once speculated that the Nebraska Republican could join a presidential ticket with Mr. Bloomberg.

Messrs. Obama and Bloomberg spoke before the speech yesterday for about 15 minutes, and Mr. Obama picked the mayor’s brain on “how decisions are made on Wall Street,” Mr. Loeser said.

Mr. Obama has made by far the most public push for Mr. Bloomberg’s backing of any remaining candidate since the mayor announced he had changed his mind and would consider a public endorsement. Mr. Bloomberg has in turn been mentioned as a possible vice presidential pick should Mr. Obama secure the nomination.

In what his campaign billed as a major economic address, Mr. Obama called for an overhaul of financial regulatory policy in the wake of the subprime mortgage crisis, blaming a Clinton-era law for leaving Wall Street ill-equipped to deal with the current economic woes.

Mr. Obama said institutions that look to taxpayers for lines of credit must be subject to regulation, and he proposed a new independent commission to oversee financial markets. His plans were thin on specifics, however, leading to criticism from both the Clinton and McCain campaigns that he was offering little more than “vague” platitudes when concrete proposals were needed.

“At a time of crisis in our financial markets, Senator Obama announced a series of broad, vague principles, while offering no new concrete solutions to provide Americans with greater confidence in the market or keep them in their homes,” Senator Clinton’s policy director, Neera Tanden, said in a statement.

An adviser to Senator McCain, Douglas Holtz-Eakin, said that while there was not “grand disagreement about the need for effective regulation … the devil will be in the details.” He was much more critical of Mr. Obama’s plan for a $30 billion housing stimulus package. Speaking both of Mr. Obama and Mrs. Clinton, who has proposed a similar fund, Mr. Holtz-Eakin said: “Their instincts are beginning to match their liberal records.”