The body of Mr Peres, who died on Wednesday aged 93, is lying in state ahead of his funeral on Friday.
A huge security operation is under way for the ceremony in Jerusalem which will be attended by world leaders including US President Barack Obama.
Palestinian President Mahmoud Abbas has said he also plans to attend.
Thousands of Israelis passed by Mr Peres's coffin outside the Knesset (parliament) throughout the day to pay their respects.
"It's important that my children understand and respect what this man did, his values, his love for Israel, his want for peace," said Marielle Halimi, who waited outside for more than an hour to file past the coffin with her three children.
Earlier, Israeli leaders including President Reuven Rivlin and Prime Minister Benjamin Netanyahu placed wreaths in a solemn ceremony.
Former US President Bill Clinton also travelled directly to the Knesset in Jerusalem after flying into Tel Aviv.
Mr Clinton helped to broker the 1993 Oslo peace accords for which Mr Peres won the Nobel Peace Prize the following year along with Prime Minister Yitzhak Rabin, and Palestinian leader Yasser Arafat.
Mr Clinton referred to Mr Peres as his "brilliant friend".
Mr Abbas said that by attending Friday's funeral he wanted to "send a strong message to Israeli society that the Palestinians are for peace, and appreciate the efforts of peaceful men like Shimon Peres", a senior Palestinian official said.
The Palestinian delegation will include chief negotiator Saeb Erekat and security chief Majid Faraj.
Other leaders set to attend include UN Secretary General Ban Ki-moon, German Chancellor Angela Merkel, French President Francois Hollande, Canadian Prime Minister Justin Trudeau, Australian Prime Minister Malcolm Turnbull and Mexican President Enrique Pena Nieto.
Mr Peres was one of the last of a generation of politicians present at Israel's birth in 1948.
He suffered a stroke two weeks ago and died on Wednesday in a hospital near Tel Aviv.
The funeral ceremony will be held at Mount Herzl Cemetery in Jerusalem.
Long queues have formed outside the Israeli parliament as people pay their respects to former Prime Minister and President Shimon Peres.