, 93, suffered a stroke with "a component of bleeding," Dr. Yitzhak Kreiss said Tuesday.
"After the completion of doctors' consultations held a few minutes ago, it was decided that there is no indication at this stage that would justify surgery," the statement said.
He will remain sedated and intubated in the intensive care unit at Sheba Medical Center in Ramat Gan.
Peres' family remained hopeful amid the news.
"My father is a special man. I remain optimistic although these are not simple hours," Peres' son, Chemi, 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. And I will take this opportunity on his behalf to send all of you his love."
Peres retired from public office in 2014 after his seven-year term as president ended. By then, he had been in Israeli politics for more than half a century, holding virtually every position in Israel's Cabinet, from minister of defense to prime minister, a position he held twice.
He battled Israeli Prime Minister Yitzhak Rabin for Labor Party leadership in the 1980s and 1990s, eventually becoming Rabin's foreign minister. In that role, Peres concluded the Oslo Peace Accords, for which he was awarded the Nobel Peace Prize in 1994
with Rabin and Yasser Arafat.
After Rabin was assassinated in 1995, Peres became prime minister, calling early elections so the government would have a mandate to pursue a two-state solution. But a wave of Palestinian suicide attacks left Peres struggling to defend the peace process, ultimately costing him the next election.
As Israel's ninth president, he addressed the Turkish parliament in 2007, becoming the first Israeli president to speak to a Muslim country's legislature. He called for peace talks in 2011 with the Palestinians and warned the United Nations against recognizing Palestine as an independent state outside a peace plan.
He received the US Presidential Medal of Freedom in 2012 from President Barack Obama.
He has remained in the public eye since leaving office, continuing his work for peace in the Middle East.
In a 2015 interview with CNN, Peres expressed support for a nuclear deal with Iran and said it would be feasible for inspectors to enforce the terms of the agreement.
In July he laid the cornerstone for the Israeli Innovation Center at the Peres Peace House in Tel Aviv with President Rivlin and Prime Minister Benjamin Netanyahu. The center aims to showcase Israel's technology achievements and encourage entrepreneurs and start-ups.
Tuesday's news is the latest health scare for the elder statesman.
Peres was rushed to the hospital in mid-January after suffering a minor heart attack. He underwent emergency surgery and got a stent, but would not be slowed down, asking the doctor how soon before he would be up and running again. He returned to the hospital 10 days later after suffering from an irregular heartbeat.