Otto Warmbier from Ohio confessed to attempting to take the banner from a staff-only section of the Yanggakdo International Hotel in Pyongyang.
The 21-year-old University of Virginia undergraduate admitted planning to give it to another member of his church in Wyoming as a "trophy".
North Korea announced in January it had arrested Warmbier and it accused him of committing an anti-state crime with "the tacit connivance of the US government and under its manipulation".
Warmbier went against advice from the US government by visiting North Korea with Young Pioneer Tours, an agency specialising in travel to the country.
People previously held in North Korea have often later recanted their public confessions following their release.
#PRAY with us @VOMC for Otto Warmbier who is held in #NorthKorea for 'stealing' for his church. @wwmonitor reports: https://t.co/189MYiMR8f
— Voice of the Martyrs (@VOMC) 29 February 2016
Mr Warmbier's parents spoke of their relief to see a picture of their son, claiming they hadn't heard from him since his arrest.
In a statement provided by the University of Viriginia, Mr Warmbier's father, Fred Warmbier, said: "You can imagine how deeply worried we were and what a traumatic experience this has been for us.
"I hope the fact that he has conveyed his sincere apology for anything that he may have done wrong will now make it possible for the (North Korean) authorities to allow him to return home."
The pastor of Warmbier's church, the Friendship United Methodist Church in Wyoming, Meshach Kanyion, declined to comment.
Speaking to reporters in Pyongyang, Mr Warmbier also said he had been encouraged in his act by the University of Virginia's "Z Society", described by the university's alumni associations as a "semi-secret ring society"
The US and South Korean governments are regularly accused by North Korea of sending spies to overthrow it's government.