WASHINGTON—House Speaker Paul Ryan said Thursday that the chamber’s chaplain will remain in his post and he will no longer seek his resignation, after the chaplain publicly questioned why he was being asked to step aside and reversed his earlier decision to quit.

Mr. Ryan’s decision could defuse growing tensions over the chaplain’s fate. The news of the Rev. Patrick Conroy’s resignation last month roiled the House, with many lawmakers pressing for an explanation about why he was asked to resign by Mr. Ryan.

Mr....