Nationwide concern mounted over the condition of 93-year-old Peres, widely respected as an elder statesman both in Israel and abroad.
Peres suffered "a major stroke today with a component of bleeding," Dr. Yitzhak Kreis told journalists late Tuesday outside the hospital near Tel Aviv where he was being treated.
He was sedated in the intensive care unit, said Kreis, director of the Sheba Medical Centre at Tel HaShomer in Ramat Gan.
A later statement from Peres's office said he was in serious but stable condition, with doctors having decided not to operate for the time being.
Israeli newspaper Haaretz quoted the head of the hospital's stroke unit as saying "the damage isn't the main issue currently."
"We're working on getting him to a state in which his life won't be in jeopardy," Dr. David Orion said.
Peres's son Chemi told journalists that "we are going to have to take difficult decisions apparently later, but not yet."
"Myself and my family members are going through difficult times, difficult hours," he said.
"I know that my father did not care about anything as much as he cares about people, as much as he cares about Israel, the Jewish people, and the people in Israel," he said.
"And I will take this opportunity on his behalf to send all of you his love."
Last founding father
The last of Israel's founding fathers, Peres has held nearly every major office in the country, including prime minister twice and president, a mostly ceremonial post, from 2007 to 2014.
A former hawk turned dove, the highlight of his career came in 1994, when he was awarded the Nobel Peace Prize along with Yitzhak Rabin and the late Palestinian leader Yasser Arafat for his role in negotiating the Oslo accords with the Palestinians.
The first of the Oslo accords was signed exactly 23 years ago Tuesday -- September 13, 1993. Rabin was assassinated two years later.
Statements of concern flooded in from the country's politicians and around 40 journalists gathered outside the hospital, Israel's largest, awaiting word on his treatment.
Prime Minister Benjamin Netanyahu had spoken with the director of the hospital to receive an update, a spokesman said.
"The prime minister conveyed the prayers of the entire nation for a quick recovery," his office said.
Netanyahu said on his twitter account: "Shimon, we all love you".
President Reuven Rivlin said in a statement he was "following with concern the updates from the hospital, and pray together with the entire people for my friend Shimon's recovery."
Opposition leader Isaac Herzog also wished the elder statesman a rapid recovery.
Nickolay Mladenov, UN special coordinator for the Middle East peace process, said he was praying for Peres, calling him "a patriarch of peace and progress."
Daily gymnastics
In January, Peres was hospitalised twice for heart trouble.
In the first instance, the hospital said he had suffered a "mild cardiac event" and underwent catheterisation to widen an artery.
He was rushed to hospital a second time days later with chest pains and an irregular heartbeat.
Peres has sought to maintain an active schedule despite his age, particularly through events related to his Peres Center for Peace.
When leaving hospital on January 19, Peres said he was keen to get back to work.
"I'm so happy to return to work, that was the whole purpose of this operation," he told reporters.
He met US Vice President Joe Biden during a visit to Israel in March.
He once confided that the secret to his longevity was daily gymnastics, eating little and drinking one or two glasses of good wine.
Having earlier hawkishly rejected any compromise with hostile Arab states, he said he was converted after 1977, when Egyptian president Anwar Sadat made a historic visit to Jerusalem, leading to the first Arab-Israeli peace treaty.
Born in Poland in 1923, Peres emigrated to what was then British mandatory Palestine when he was 11.
He joined the Zionist struggle in the 1940s and while hitchhiking met David Ben-Gurion, who would become Israel's first prime minister.
He became director general of the nascent defence ministry at only 29 years old.
Beyond his accomplishments in the public eye, Peres was also seen as a driving force in the development of Israel's undeclared nuclear programme.
