“I don’t know how this will be misconstrued by the press,” Mr. Rangel said. “But no matter what they say, I go back to Washington a stronger man than I have ever been.”

He also reaffirmed his commitment to the president’s agenda.

“In the time we are at in our history, President Obama needs people like me more than ever,” Mr. Rangel said. “I’ll go back to tell the president, ‘You don’t need those Republicans, and there are a lot of Democrats who got elected, but they vote Republican.’ ”

Mr. Rangel was presented with a victory cake, a gift from Aretha Franklin.

The last time Mr. Rangel faced a serious primary challenge was in 1994, when he defeated Mr. Powell, who was then a councilman, 61 percent to 33 percent. He has otherwise cruised to re-election.

In the general election, Mr. Rangel will face a Republican, Michel J. Faulkner, a minister who founded the New Horizon Church of New York in Harlem, and Craig Schley, 46, a former intern for Mr. Rangel, who is running on the Independence Party line.

Despite his victory, Mr. Rangel’s troubles are hardly over, as a House panel in Washington prepares to convene a public trial of Mr. Rangel, 80, later this month on 13 counts of ethics violations.