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Ex-Pope Benedict XVI is "lucid and alert" but still in a serious but stable condition, the Vatican has said.
Pope Francis warned on Wednesday that his 95-year-old predecessor was very ill and appealed to everyone to pray for him.
The Vatican said on Thursday that the former Pope "was able to rest well last night".
Benedict XVI became the first leader of the Catholic Church to stand down in 600 years in 2013, citing advanced age.
When he was elected Pope in 2005 at the age of 78 he had earned a reputation as a conservative enforcer of Church doctrine.
Born Joseph Ratzinger, he was the first German Pope for 1,000 years, but his health was already in decline and within eight years he decided he no longer had the ability to fulfil his office properly.
After Pope Francis alerted the world to his predecessor's failing health, the Vatican put out an initial statement confirming there had been an "aggravation" due to advancing age. In a further statement, on Thursday, it said "although his condition remains serious, the situation at the moment is stable".
The Pope visited Benedict on Wednesday at the Mater Ecclesiae monastery, within the Vatican walls, and where he has lived since he stepped down. The former Pope is now under the constant supervision of doctors.
Little is known about his condition and Italian news agency Ansa quoted sources as saying nothing has changed in the past 24 hours.
Benedict has lived at Mater Ecclesiae, a converted convent, since Francis was elected Pope in March 2013.
Although he had been suffering from poor health, his decision to resign came as a surprise as no pope had done so since Gregory XII in 1415.
His papacy was marked by a scandal involving child sexual abuse by priests. Two reports in 2009 detailed the extent of paedophilia and cover-ups within the Irish Church - and it later emerged that almost 400 priests had been defrocked by Benedict in 2011 and 2012.
Earlier this year the former Pope accepted that errors had been made in handling sexual abuse cases while he was Archbishop of Munich from 1977 to 1982.
A German inquiry commissioned by the Church found that he had failed to act in four cases. Benedict denied wrongdoing but asked forgiveness for any "grievous fault".