(CNN) -- Texas conservative Pete Sessions has dropped out of the running to replace Rep. Eric Cantor as the No. 2 Republican in the House leadership.
"After thoughtful consideration and discussion with my colleagues, I have made the decision to not continue my run for House majority leader," Sessions said in a statement.
"Today, it became obvious to me that the measures necessary to run a successful campaign would have created unnecessary and painful division within our party," he continued.
Sessions, in appealing directly to the conservative base of the GOP, argued initially that he should succeed Cantor on the leadership roster because he is a red-state Republican who can bring that sensibility to the party hierarchy.
Cantor lost his primary on Tuesday in Virginia in stunning fashion, and will leave the leadership post at the end of July.
House Majority Whip Kevin McCarthy of California is considered the frontrunner to succeed him in a vote next Thursday. Cantor endorsed McCarthy.