WASHINGTON — Speaker Paul D. Ryan reinstated the Rev. Patrick J. Conroy as the chaplain of the House of Representatives on Thursday, after the chaplain sent him a letter rescinding his forced resignation and daring the speaker to fire him.

“I have accepted Father Conroy’s letter and decided that he will remain in his position as chaplain of the House,” Mr. Ryan said in a statement. He added, “It is my job as speaker to do what is best for this body, and I know that this body is not well served by a protracted fight over such an important post.”

Father Conroy, a Catholic priest who has been the chaplain since 2011, intimated in a letter to Mr. Ryan on Thursday that the speaker did not have the authority to fire him, noting that the chaplain, who is selected by the speaker, is elected by the members of the House. He suggested his Catholic faith had contributed to his dismissal.

And in an interview, Father Conroy said he had hired a lawyer to press his case. “This is so contentious, and I think it is so historic,” Father Conroy said, adding, “It’s not over.”