Israelis have been watching closely since their elder statesman and last remaining founding father was hospitalised on Tuesday feeling unwell and then suffered a stroke and internal bleeding.
His condition has improved since, but he remained sedated on Friday morning.
"There is no change at the moment," a spokesman for Peres said.
"His condition is obviously still serious but at the moment he is stable."
Doctors are hoping it will be possible to take Peres out of sedation in the coming days, though they are monitoring his condition hourly.
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He has not been able to speak due to being intubated, Walden said.
Peres has held nearly every major office in Israel, serving twice as prime minister. He was president, a mostly ceremonial role, from 2007 to 2014.
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.
Pope Francis wrote to Peres yesterday 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.
Peres and the Pope last met two months ago when Peres visited the Vatican, while in 2014 they made a joint prayer for peace alongside Palestinian president Mahmud Abbas.
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.