"There is another real improvement today," Peres's personal physician and son-in-law Rafi Walden told AFP, describing his condition as serious but stable.
He said it was likely his condition would remain that way for the coming days.
Peres remained in intensive care and was breathing with the help of a respirator, but was still able to respond to prompts as he had the previous day.
The last of Israel's founding fathers, Peres has held nearly every major office in the country, serving twice as prime minister. He was president, a mostly ceremonial role, from 2007 to 2014.
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