Cheney blurted out the "F word" at Democratic Senator Patrick Leahy of Vermont during a heated exchange on the Senate floor on Tuesday, his aides said.
The terse discussion between the two ended with Cheney finally telling Leahy to "f... off" or "go f... yourself", the aides said.
"I think he was just having a bad day," Leahy was quoted as saying on CNN, which first reported the incident. "I was kind of shocked to hear that kind of language on the floor."
"That doesn't sound like language the vice-president would use but there was a frank exchange of views," said Cheney spokesman Kevin Kellems.
According to congressional aides, Leahy said "hello" to Cheney following the taking of the Senate group photo on the floor of the chamber.
Cheney then ripped into Leahy for the Democratic senator's criticism this week of alleged war profiteering in Iraq by Halliburton, the oil-services company that Cheney once ran.
Leahy and other Democrats have called for congressional hearings into whether the vice-president helped the firm win lucrative contracts in Iraq after the US-led invasion of the oil rich country.
During their exchange, Leahy noted that Republicans had accused Democrats of being anti-Catholic because they are opposed to some of President George Bush's anti-abortion judges, the aides said.
That's when Cheney unloaded with the "F-bomb", aides said.
According to Senate rules, profanity is not permitted in the chamber. But when the exchange occurred between Leahy and Cheney, the Senate was not in session, so there was technically no foul.