"Our consular officers in Burma have sought to visit Daniel, but we have not been afforded access to him by regime officials," Price said in a telephone briefing.
Fenster, 37, worked as the managing editor of the Frontier Myanmar news magazine.
He was detained on May 24 at Yangon International Airport before he could board a plane to leave the country.
Media reported that earlier on Thursday, Fenster appeared before a special court in Yangon's Insein Prison to face charges under a law that criminalises encouraging dissent against the Myanmar military.
The military in Myanmar seized control of the nation in a coup d'état on Feb 1, 2021. There have been mass protests since the coup was staged. On the other hand, the military authorities assert that it was justified and vow to transfer power after a new election, the date for which however is yet to be given. - Bernama