Hartmann, a German Catholic priest, wants to remain ordained, but wrote on Facebook that he wants to be released from his celibacy oath.
"I still feel it is my calling to be a Catholic priest, a pastor and a theologian," he wrote.
In January 2014, Hartmann revealed on a televison talk show that he had a secret daughter, born in 1989. He was asked by his superiors to step down from his north Bavarian parish shortly thereafter.
In his Facebook post, Hartmann stated that he desires a relationship with the mother of his daughter, and has not been able to practice celibacy.
"After [my daughter's birth] I tried to walk the road of celibacy again, but since 2007 I have realized more and more that I am just not up to it," he said. "I have known for some years now that the oath I took after just two and a half years of seminary training was too rushed, and did not reflect the constitution of my character."
Hartmann vowed celibacy in 1981, eight years before his daughter was born.
The priest urged Pope Francis to "bring solution" and "relief" to those who wish to remain in the priesthood, but do not want to be celibate. He also called coupling a fundamental right.
"There is a human right to partnership, marriage and parenthood," he wrote, "even if you can forego it willingly for religious reasons."
Although his daughter is now 24-years old, Hartmann expressed a desire for her to have married parents.
He wrote that the primary reason for his request was "above all to allow me to go into a marital partnership into which my daughter can be integrated as part of a family".
The Vatican has not responded to Hartmann's open letter.