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 Beatitude's condition is assessed as critical by the attending physicians," the medical report from the hospital stated.
On Saturday, his condition was assessed as "stable despite his already complicated medical history".
Anastasios is credited with having revived 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 reported that he was also suffering from gastric bleeding.
In November 2020, he was hospitalised in Athens for 12 days with Covid-19.
Greek Prime Minister Kyriakos Mitsotakis visited Sunday afternoon the hospital where Archbishop Anastasios of Albania is being treated and was informed for the ailing archbishop's health condition.
