Rep. Tony Gonzales, R-Texas, speaks during a House Homeland Security Committee hearing on Feb. 10 in Washington, D.C. Samuel Corum/Getty Images hide caption

Samuel Corum/Getty Images

House Republican leaders have called on Rep. Tony Gonzales, R-Texas, to end his bid for reelection, as the third-term lawmaker continues to face fallout over allegations of a past affair with a member of his staff.

The announcement from Republican leadership follows the decision by the House Ethics Committee to launch a formal investigation into Gonzalez, who earlier this week was forced into a May runoff in the Republican primary in his district.

"Congressman Gonzales has said he will fully cooperate with the investigation," House Speaker Mike Johnson, R-La., House Whip Tom Emmer, R-Minn., and Conference Chair Lisa McClain, R-Mich. wrote in a statement. "We have encouraged him to address these very serious allegations directly with his constituents and his colleagues.…