An independent congressman, Eittel Ramos, challenged Mr Waisman to a duel with pistols, saying the vice president had insulted him after he criticised comments by President Alexander Toledo's wife, Eliane Karp.
Mr Waisman said he was a civilised and peaceful man and his moral beliefs prevented him from trying to end another's life.
It is not clear if duels are legal in Peru - the country's last political duel was in 1957, when a future president, Fernando Belaunde, drew swords against a rival politician.
Beach duel
The trouble started earlier this month when Mr Ramos criticised first lady Eliane Karp for saying "two-bit parties" were trying to undermine her husband.
The vice president "called my attitude cowardly because I said what I said about a woman," Mr Ramos was quoted as saying by Reuters news agency.
He said the invitation to Mr Waisman to a duel with pistols on a Lima beach was a matter of honour for him.
"If the gentleman insulted me and called me a coward, I have the right to demand... a duel. Since I am the injured party, I choose the weapons and the place," he said.
"I'm not backing down... unless he apologises publicly," Mr Ramos said.
No date has been proposed for the duel, but Mr Ramos said he had already chosen a doctor friend to be his second.
Peru's last political duel took place in 1957, when Fernando Belaunde - who went on to be president from 1963-68 and 1980-85 - fought a political rival with swords.
The referee ended the duel when Mr Belaunde nicked his rival, drawing blood.
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