"Let's say I believe firmly in Ronald Reagan's 11th commandment: Thou shalt not speak ill of a fellow Republican," Cheney said. "But it's very hard sometimes to adhere to that where Chuck Hagel is involved."
Cheney's comments came in a Newsweek interview released Sunday.
Hagel, a potential presidential candidate, has been outspoken in his criticism that the Republican White House lacks a coherent strategy in Iraq.
His "ping-pong" remark came Wednesday as the Senate Foreign Relations Committee debated a nonbinding resolution that condemned President George W. Bush's troop buildup in Iraq. Hagel co-sponsored the measure, which the committee approved in a 12-9 vote. He was the only Republican to vote for it.
In the interview, Cheney also said he doesn't spend any time worrying about how the public or the media view him. When pressed to react to personal criticism from people with whom he has worked before, Cheney said: "Well, I'm vice president and they're not."