That Democrat, Charles "Champ" Walker Jr., called the speaker's story a fabrication and demanded an apology.

Speaking at a fund-raiser for Mr. Burns in Savannah, Mr. Hastert said Mr. Walker approached him in Washington in September after a late dinner at the popular Capitol Hill hangout Old Ebbitt's Grill.

"He came over and introduced himself and said, 'I'm Charles Walker. I'm going to be the next congressman from the 12th District in Washington,"' Mr. Hastert said. "I said, 'Excuse me, sir, but I don't know that that election has happened yet."'

Mr. Hastert said the story illustrates how Democrats see as a "slam-dunk" their chances of winning the 12th Congressional District, drawn by state lawmakers as an open seat packed with Democratic voters.

"I'd never be so presumptuous to tell someone I've already won," Mr. Walker said in a telephone interview. He also denied meeting Mr. Has-tert.

"I can say without any equivocation that I've never met Rep. Hastert at any point in time," Mr. Walker said. "To flat out tell a lie about meeting someone, it's hypocritical when they keep saying integrity is paramount. ... I think the speaker needs to apologize."

Mr. Walker's campaign says he visited Washington from Sept. 12-14 with his father, state Sen. Charles Walker.

It's possible Mr. Hastert got the two Walkers confused, said Walker spokesman John Kirin-cich. The elder Mr. Walker did eat at Old Ebbitt's Grill and sat at a table adjacent to Mr. Hastert's, Mr. Kirincich said. But the elder Mr. Walker also denied speaking to him.

"No communication passed between the two of them," Mr. Kirincich said. "The most (Mr. Walker) could think of is perhaps Hastert overheard part of their conversation. Perhaps he didn't know there were two Charles Walkers."

Hastert spokesman John Feehery did not return a telephone message left at his home seeking comment.

While speaking at the $100-per-plate event Sunday, Mr. Hastert took aim at Mr. Walker and Democratic lawmakers who designed the 12th District.

"When the Democrats drew this district, they thought it was a slam-dunk for them," Mr. Hastert told reporters. "We don't take anything for granted. When a seat's open in the Congress, it's important to us."

Republicans hold a five-vote majority in the House and are trying to protect and improve on those numbers in the Nov. 5 elections.

Mr. Burns, a Sylvania college professor who pulled off an upset victory over Barbara Dooley of Athens in the GOP primary, says he can do the same against Mr. Walker in the general election.

The 12th District, which sprawls 200 miles from Athens to Augusta to Savannah, has a voting-age population that's 37 percent black. Black voters generally side with Democrats.

A handful of black Savan-nahians attended Mr. Burns' fund-raiser Sunday at an Anheuser-Busch distributing plant, but not all of them were in Mr. Burns' corner.

"I'm supporting Champ Walker," said the Rev. Leonard Small, a black minister who attended at the invitation of local Republican officials. "My mind's basically made up."

Mr. Burns criticized Mr. Walker for turning down a debate on statewide television Sunday night. Mr. Burns planned to appear at the Atlanta debate alone.

Also, Mr. Burns denied accusations by Mr. Walker's campaign that he wants to abolish Medicare and the Department of Education.

Mr. Burns has signed a pledge with the Republican Liberty Caucus, a political action committee that on its Web site calls for ending the entitlement to Medicare and dismantling several federal agencies.

Mr. Burns said the pledge he signed included no promises to abolish any programs. He said he wants to strengthen Medicare and improve the Department of Education while cutting its bureaucracy.

"I'm going to support Medicare. I always have; I always will," Mr. Burns said.

Mr. Walker said he could not attend the Atlanta debate because of a scheduling conflict with the opening of a new campaign office in Augusta. He accused Mr. Burns of ducking previous candidate forums.