From CNN Ticker Producer Alex Mooney

WASHINGTON (CNN) -- House Speaker Dennis Hastert Tuesday said he would fire anyone on his staff found to have covered up complaints about former Rep. Mark Foley's email messages with teenage House pages.

The Illinois Republican also said his staff handled the matter "as well as they should," but acknowledged they could have handled the matter better.

"In 20-20 hindsight we could probably do everything better, but if there was a problem, if there was cover-up then we should find that out through the investigation process." Hastert said in a press conference in Aurora, Illinois. "They will be under oath, and we'll find out if they did cover something up, then they should not continue to have their jobs."

Hastert also said he is unaware of what Arizona GOP Rep. Jim Kolbe, a former member of the board that oversees the House page program, knew about Foley's inappropriate advances.

"He was on the page board, that was his job to do that, that confrontation, I don't know anything more about it," Hastert said. "If it was something of a nature that should have reported or brought forward, then he should have done that."