Peres, 93, is in severe but stable condition, and is intubated and sedated, following Tuesday's stroke, said Dr. Yitshak Kreiss, manager of Sheba Medical Center in Ramat Gan, where Peres is being treated.
"He is slightly more alert, and it is our impression that his neurological condition is a little bit better," Kreiss said Wednesday afternoon at the hospital.
Kreiss wasn't alone in sounding a cautiously optimistic view of Peres' condition. Peres' son-in-law and personal physician, Dr. Rafi Walden, said the veteran politician and Nobel laureate "responded very well" as his sedation dosage has been reduced.
"He understood what he was told. He shook my hand energetically," Walden said. "There has been a significant improvement in his consciousness."
Israeli Health Minister Yaakov Litzman told reporters that he was "a bit more optimistic than I would have been last night" about Peres' condition.
Peres was taken to the hospital Tuesday after what Kreiss described as a stroke involving "a component of bleeding." Walden said doctors would keep Peres under mild sedation to help him rest and optimize his chances for recovery.
In Israeli politics for more than half a century
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 1992. 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.
Continued work for peace in Middle East
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 Reuven 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.