A major security operation was being put in place ahead of Friday's funeral, which is to be attended by leaders from across the world, including US President Barack Obama and Britain's Prince Charles.
In a rare visit to Jerusalem, Palestinian president Mahmud Abbas was also planning to attend, Palestinian officials told AFP.
Peres's death yesterday at age 93 after suffering a major stroke triggered an outpouring of grief and tributes that hailed the Israeli ex-president's transformation from hawk to fervent peace advocate.
Later in the day, Clinton arrived in Israel and travelled directly to view Peres's coffin, appearing moved as he stood silently before it.
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Clinton had helped usher in the Oslo peace accords of the 1990s, which resulted in the Nobel prize for Peres.
The plaza was opened to the public following the visit by the Israeli leaders, and an estimated 30,000 mourners made their way into the grounds after passing through stringent security checks.
"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 arrived with her three children and waited for more than an hour to enter before leaving in tears.
In a career spanning seven decades, Peres held nearly every major office, serving twice as prime minister and as president, a mainly ceremonial role, from 2007 to 2014.
He won the 1994 Nobel Peace Prize jointly with prime minister Yitzhak Rabin and Palestinian leader Yasser Arafat for his role in negotiating the Oslo accords, which envisioned an independent Palestinian state.
Around 8,000 police were being deployed for the commemorations today and Friday, and roads were being closed in Jerusalem.