Washington ? House Speaker Dennis Hastert, R-Ill., said Tuesday that he believes his staff has handled the Mark Foley matter properly, but “if they did cover something up, then they should not continue to have their jobs.”

Hastert’s remarks came amid a quickening pace of investigations into Foley’s relationships with teenage congressional pages and the House’s handling of warnings about the former congressman’s behavior. FBI agents interviewed former House page Jordan Edmund in Oklahoma City, and Foley’s former chief of staff, Kirk Fordham, is scheduled to speak with House ethics committee members and staffers Thursday.

Edmund was among the male pages who received sexually explicit instant messages from Foley, a six-term House Republican from Florida. Foley abruptly resigned Sept. 29, just as ABC News was airing some of the graphic exchanges.

Speaking Tuesday to reporters in Illinois, Hastert again said he knew nothing of alarms raised in some circles about Foley’s behavior toward pages until the day he resigned. Two high-ranking GOP House members have said they mentioned to Hastert concerns about 2005 e-mails that Foley sent to a former page from Louisiana. The speaker’s office says two of his high-ranking aides – counsel Ted Van Der Meid and deputy chief of staff Mike Stokke – also knew of those e-mails but did not inform Hastert.

Hastert said he recalls no such conversations with colleagues. He said his aides have “handled it as well as they should.”

He added: “In 20/20 hindsight, probably you could do everything a little bit better. … If anybody’s found to have hidden information or covered up information, they really should be gone.”