Story highlights Israeli Health Minister Yaakov Litzman says he is more optimistic about Peres' condition

Former Israeli Prime Minister Shimon Peres suffered stroke on Tuesday

Tel Aviv, Israel (CNN) Former Israeli President and Prime Minister Shimon Peres' condition has improved somewhat a day after his stroke, and he was able to shake his son-in-law's hand as physicians reduced his level of sedation, doctors said Wednesday.

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."

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