"How's your boy?" Webb, in an interview Wednesday, recalled Mr. Bush asking during the reception two weeks ago.
"I told him I'd like to get them out of Iraq," Webb said.
"That's not what I asked. How's your boy?" the president replied, according to Webb.
At that point, Webb said, Mr. Bush got a response similar to what reporters and others who had asked Webb about Lance Cpl. Jimmy Webb, 24, have received since the young man left for Iraq around Labor Day: "I told him that was between my boy and me."
Webb, a leading critic of the Iraq war, said that he had avoided the receiving line and photo op with Mr. Bush, but that the president found him.
The White House had no comment on the reception. But it did not dispute an account of the exchange in Wednesday's Washington Post.
Webb, a Marine veteran of the Vietnam War and Navy secretary under President Reagan, defeated Republican Sen. George Allen by 9,329 votes out of 2.37 million cast, giving the Democrats control of both houses of Congress for the first time since 1994.
Webb left the GOP, in part over the Iraq war. He warned against the invasion, and criticized Mr. Bush over Iraq during the Senate campaign.
He said he meant no disrespect to the presidency during the reception, but "I've always made a distinction about not speaking personally about my son."
In interviews during the campaign, Webb said it was wrong to elevate the role of one Marine over others. Webb also expressed concern that a high profile could subject a Marine to greater peril.
He wore his son's buff-colored desert boots throughout the campaign, but refused to speak extensively about his son's service or allow it to be used in campaign ads.