Archbishop Anastasios, 95, was taken to the Greek capital on Friday evening, four days after being admitted to hospital in Tirana with what Church officials called a "seasonal virus".
"His health condition, despite his already complicated medical history, is considered stable and is being closely monitored," Evangelismos said.
"His Beatitude is undergoing the necessary medical examinations and is receiving appropriate care."
Anastasios is credited with reviving the Orthodox Church in Muslim-majority Albania. He has led the Church there for three decades.
He was airlifted to Athens on a C-27 Greek air force plane "following a request from Greek emergency services", the defence ministry said.
Greek public television ERT said he was also suffering from a "gastric hemorrhage".
In November 2020, he was hospitalised in Athens for 12 days with Covid-19.