Vice President Cheney objected yesterday to Sen. John McCain's assertion that Donald H. Rumsfeld "will go down as one of the worst secretaries of defense in history" and added that the senator had apologized to him for saying Cheney had misled President Bush on Iraq.

Cheney, speaking in an interview with ABC News yesterday during a week-long swing through Asia, said he "fundamentally disagrees" with the Arizona Republican's statement Monday about Rumsfeld, made while McCain was campaigning for president in South Carolina.

Bush replaced Rumsfeld in November after Democrats captured both chambers of Congress, a move that many congressional Republicans believe the president should have made before the election as the situation in Iraq soured. Although Rumsfeld's refusal to send a larger force to Iraq early in the invasion is seen by some as a crucial mistake, Cheney has maintained that Rumsfeld did an outstanding job under trying circumstances.

"I think Don's a great secretary. I know a little bit about the job," said Cheney, a former defense secretary. "I've watched what he's done over there for six years. I think he did a superb job in terms of managing the Pentagon under extraordinarily difficult circumstances."

Cheney also countered McCain's assertion that the vice president misled Bush when it came to Iraq. "John said some nasty things about me the other day, and then next time he saw me, ran over to me and apologized," Cheney said. "Maybe he'll apologize to Rumsfeld."

McCain is expected to formally announce next month his second run for the White House. Long a vocal advocate of putting more troops into Iraq, he has strongly endorsed Bush's decision to send 21,500 additional combat troops to Iraq even as he has harshly criticized Rumsfeld and Cheney for the way the war has been waged.

"The president listened too much to the vice president," McCain told the Politico last month. ". . . Of course, the president bears the ultimate responsibility, but he was very badly served by both the vice president and, most of all, the secretary of defense."

In his interview, conducted aboard the USS Kitty Hawk at Yokosuka, Japan, Cheney said he encountered McCain in the Senate chambers. "Well, he came up to me on the floor a couple of days later, the next time I was on the floor of the Senate, said he'd been quoted out of context, and then basically offered an apology, which I was happy to accept," the vice president said.

McCain declined to comment on Cheney's remarks. "The senator's position on the war is well known," said Danny Diaz, McCain's spokesman.