"The Pope Emeritus was able to rest well last night, he is absolutely lucid and alert and today, although his condition remains serious, the situation at the moment is stable," the Vatican press office said Thursday.
"His situation has not changed from yesterday," an unnamed source in contact with those around the German ex-pontiff told ANSA news agency, adding that doctors were continually monitoring his health.
Contacted by AFP, the Vatican neither confirmed or denied the report.
Benedict, who in 2013 became the first pope since the Middle Ages to resign as head of the worldwide Catholic Church, has been in fragile health for many years.
But Pope Francis sparked alarm on Wednesday by revealing at his general audience that his predecessor, whose birth name is Joseph Ratzinger, was "very ill".
He called for people to pray for him, before going to visit Benedict at the monastery in the Vatican grounds where he lives.
The Vatican later confirmed his health had worsened, while a Vatican source told AFP on Wednesday that it began deteriorating "about three days ago".
"It is his vital functions that are failing, including his heart," the source said, adding that no hospitalization was planned, as he has the "necessary medical equipment" at home.
Benedict had cited his declining physical and mental health in his decision to stand down.
His resignation created an unprecedented situation in which two "men in white" -- Benedict and Pope Francis -- have co-existed within the walls of the tiny city state.
Benedict was 78 when he succeeded the long-reigning and popular John Paul II in April 2005.
He was known for being a brilliant theologian, but his papacy was beset by Church infighting and the outcry over clerical sex abuse of children.
Toward the end of his papacy, it was shaken by a scandal dubbed "Vatileaks" in which leaked documents show infighting among Benedict's aides and general dysfunction at the heart of the Church's central administration, known as the Curia. The scandal exposed financial corruption and allegations about the existence of a so-called "gay lobby" that used blackmail to protect its members.
A January, 2022 independent report in Germany alleges Benedict failed to act against four cases of sexual abuse in his archdiocese when he was Archbishop of Munich between 1977 and 1982. Benedict later acknowledged errors occurred and asked for forgiveness.
This report was prepared with data from Reuters and Agence France-Presse.