"The guy saw me in almost a dozen settings, and joked with me about a bunch of things, including details of my kids. Perhaps he has forgotten everything, who knows," Abramoff wrote in an e-mail to Kim Eisler, national editor of the Washingtonian magazine.
Abramoff added that Mr. Bush "has one of the best memories of any politician I have ever met … though of course he can't recall that he has a great memory!"
Portions of the e-mails were made public Thursday by a liberal Web site, thinkprogress.org.
The New York Times reports Eisler acknowledged sharing the e-mails with a writer for the site, but didn't realize they would be made public.
"I considered them confidential e-mails, and it was a slip on my part to release a portion of them," Eisler said.
Abramoff has pleaded guilty in a fraud and bribery case and is now helping prosecutors investigate lawmakers, congressional aides and administration officials his team used to lobby.
In the e-mails, Abramoff, who raised more than $100,000 for Mr. Bush's re-election campaign, said he was even invited to Mr. Bush's Texas ranch in 2003.
"Yes, I was invited, during the 2004 campaign. It was Saturday Aug. 9, 2003 at the ranch in Crawford," Abramoff said.
He said he did not attend because he does not travel on the Jewish Sabbath.
Mr. Bush has said he doesn't recall ever meeting Abramoff, though the White House acknowledges that Abramoff attended "a few staff-level meetings" at the White House and Hanukkah receptions in 2001 and 2002.
Last month, the Washingtonian and Time magazines reported the existence of about a half-dozen photos showing the two together at various White House functions.
Asked about the e-mail messages Thursday, White House press secretary Scott McClellan said, "I think what the president says still stands: Mr. Abramoff is someone who was involved in wrongdoing, he has acknowledged that himself."
Also Friday, an Associated Press report showed that the Democrat who's been leading the attacks portraying Abramoff's activities as a Republican scandal had extensive contacts of his own with the lobbyist.
Senate Democratic leader Harry Reid wrote at least four letters helpful to Indian tribes represented by Abramoff. The Nevada senator's staff also regularly had contact with the lobbyist's team about legislation affecting other clients.
The activities are detailed in billing records and correspondence obtained by The Associated Press. They occurred over three years as Reid collected nearly $68,000 in donations from Abramoff's firm, partners and clients.
Reid's office acknowledged having "routine contacts" with Abramoff's lobbying partners and intervening on some matters, but said none of his actions were affected by donations.