Putnam, chairman of the House Republican Policy Committee, appearing on "This Week with George Stephanopoulos," said the House, the FBI and a Florida newspaper knew of what he called "odd, overly friendly e-mail" between Foley and congressional pages, but not the sexually explicit instant message exchanges discovered last month by ABC News.
Foley, R-Fla., resigned Sept. 29 over sexually explicit messages he sent to teenage male pages.
Putnam said it now was important to conduct a "full, thorough" investigation of House members and staff.
Countering Putnam's claim was Rep. Rahm Emanuel, D-Ill., also appearing on "This Week with George Stephanopoulos." Emanuel said House Republicans were trying to blame others for their problems.
A weekend Newsweek poll showed that 52 percent of respondents believe that House Speaker Dennis Hastert covered up the Foley issue, ABC News said, while 24 percent said they thought he didn't.