The 93-year-old remained sedated and on a respirator after suffering a stroke and internal bleeding on Tuesday, Peres's personal physician and son-in-law Rafi Walden told AFP.
His condition has improved since, but is still described as serious but stable.
Israeli public radio said this morning that Peres "had a quiet night" but his life remained in danger.
Israeli President Reuven Rivlin is scheduled to visit him in his hospital near Tel Aviv, after the end of the Jewish sabbath, Rivlin's office said.
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He won the 1994 Nobel Peace Prize jointly with prime minister Yitzhak Rabin and the late Palestinian leader Yasser Arafat for his role in negotiating the Oslo Accords, which envisioned an independent Palestinian state.
The former hawk turned dove is widely respected both in Israel and abroad, regularly meeting world leaders and celebrities.
Pope Francis wrote to Peres Thursday saying he had "prayed for strength for the family and for a full recovery."
The letter said the Pope held a special prayer for Peres alongside Rabbi Abraham Skorka of Argentina.
US Republican presidential nominee Donald Trump also wrote to wish Peres a "swift recovery."
"You are among the last of a generation of leaders who fought for the right of the Jewish people to shape their own destiny," Trump wrote.
Trump's Democrat rival Hillary Clinton, former British prime minister Tony Blair and Russian President Vladimir Putin have also enquired about his condition.
UN Secretary General Ban Ki-moon told the Security Council Thursday he was hoping for a "swift and full recovery," calling Peres "tireless in seeking peace between Israelis and Palestinians."
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