Olbermann repeated the offer on Monday's show and said in an interview Tuesday that he's heard no response. He said he'll continue to pursue it.
"I don't think he has the courage to even respond to this - let alone do it," Olbermann said.
Fox News Channel representatives did not respond to requests for comment.
The two men are on opposite poles of a debate that has preoccupied the worlds of talk TV and radio. Hannity says waterboarding is a fair and necessary interrogation technique for suspected terrorists; Olbermann calls it torture, says it's ineffective and should not be done by Americans.
Charles Grodin was challenging Hannity on the issue on Fox last week, and asked whether he would consent to be waterboarded.
"Sure," Hannity said. "I'll do it for charity ... I'll do it for the troops' families."
It wasn't exactly clear how serious the conversation was, since Grodin joked, "Are you busy on Sunday?" and Hannity laughed.
"I'll let you do it," Hannity said.
"I wouldn't do it," Grodin said. "I'll hand you a towel when you come out of the shower."
Olbermann's offer was quick. Besides the $1,000 per second, Olbermann said he'd double it if Hannity acknowledges he feared for his life and admits that waterboarding is torture.
"The idea of putting somebody in a position they have volunteered for, for charity, to respond to their own unsupportable claims, is in many ways priceless," Olbermann said.
Olbermann, who hasn't missed any chance to criticize his ideological enemies at Fox, concedes TV competition plays a part in his offer. But he said it was sincere, because he believes Hannity has had a damaging role in the debate.
"If you expose people to reality, even with someone who is denying reality, that can have a powerful and important impact," he said.
Copyright 2009 The Associated Press.
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