HOUSTON — Although President Obama swept into the White House with the overwhelming support of black voters, Mitt Romney appeared before the National Association for the Advancement of Colored People on Wednesday with a bold claim: “If you want a president who will make things better in the African-American community, you are looking at him.”

His assertion was met with cackles and boos — as well as tepid applause — and was emblematic of his entire speech, in which he tried to appeal to blacks while offering tough policy prescriptions that are unpopular with them.

In a roughly 25-minute speech at the N.A.A.C.P.’s annual convention here, Mr. Romney promised to fight teachers’ unions and repeal the president’s health care plan.

When he said he would “eliminate every nonessential, expensive program I can find; that includes Obamacare,” the crowd booed — the first of several instances of vocal disagreement. Mr. Romney grinned nervously and deviated slightly from his prepared remarks as he tried to explain his position.