WASHINGTON — Vice President Cheney challenges the assertion by a Republican presidential candidate, Senator McCain, that Donald Rumsfeld was one of America’s worst defense secretaries.

“John’s entitled to his opinion. I just think he’s wrong,” Mr. Cheney, who is a friend of Mr. Rumsfeld, said yesterday. He also said Mr. McCain had apologized to him for a previous comment that the vice president had “badly served” President Bush on Iraq.

“John said some nasty things about me the other day, and then next time he saw me, ran over to me and apologized. Maybe he’ll apologize to Rumsfeld,” Mr. Cheney said in an interview with ABC News.

Despite having low job approval numbers overall, Mr. Cheney continues to be very popular among rank-and-file Republicans. Many of his boosters are likely to vote in next year’s Republican presidential caucuses and primaries.

Mr. McCain, a Republican senator who lost the party’s nomination to Bush in 2000, is expected to make the formal announcement of his second run for the White House next month. He faces strong challenges from a former Massachusetts governor, Mitt Romney, and Mayor Giuliani.

Mr. McCain served more than five years as a prisoner of war in Vietnam.

Campaigning this week, Mr. McCain has talked at length with voters about Iraq and defended his staunch support of Mr. Bush’s 21,500-troop buildup there while criticizing the way the war has been managed.

“We are paying a very heavy price for the mismanagement — that’s the kindest word I can give you — of Donald Rumsfeld, of this war,” Mr. McCain said Monday. “The price is very, very heavy, and I regret it enormously.”