Rafi Walden, the son-in-law and personal doctor of Peres, said the statesman seemed "responsive" when taken out of the induced coma for a short while overnight.
"We were happy to see that when there was a short pause in the anesthetics, we realised that he's responsive, that he's probably attentive to what we're saying to him. He shook our hand," Walden said.
Kreiss said the stroke had caused "lots of bleeding".
Peres was "in serious but stable condition", doctors treating him said. In January, he had undergone a successful minor surgery at the same hospital after suffering a small heart attack.
The veteran politician was jointly awarded the Nobel Peace Prize in 1994 for his contributions in reaching an interim peace agreement with the Palestinians, along with Prime Minister Yitzhak Rabin and Palestinian leader Yasser Arafat.
The elder statesman is one of Israel's most admired symbols and the last of its founding fathers. Peres has held almost every major political office since Israel was founded in 1948, including three terms as prime minister and stints as foreign and finance minister.
He was the architect of Israel's secret nuclear programme. As a defence official in the late 1950s and early 1960s, Peres was involved in establishing the nuclear reactor in Dimona.
Concern and well wishes poured from across the political spectrum. The chief rabbis of Israel have called on the public to pray for Peres' recovery.
"Shimon, we love you and the entire nation is wishing for your recovery," Prime Minister Benjamin Netanyahu tweeted.
In a statement, President Reuven Rivlin said he was "following with concern the updates from the hospital, and pray together with the entire people for my friend Shimon's recovery.
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