The former Israeli president died on September 28 at the age of 93.
PM Benjamin Netanyahu described Shimon Peres, one of Israel’s founding fathers, as “a great man of the world”, in his funeral eulogy.
A security crackdown ahead of the funeral ceremony has led to the “preventative arrests” of several people.
Mahmoud Abbas led a delegation of senior Palestinian officials in his first visit to Israel since 2010.
As a negotiator for the Palestine Liberation Organization (PLO), Mahmoud Abbas was one of the people who signed the Oslo peace accords in 1993, for which Shimon Peres won a Nobel Peace Prize the year after, along with Yasser Arafat and Yitzhak Rabin.
A senior Palestinian official told the Associated Press that Mahmoud Abbas 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 spokesman for Hamas, the more hard-line Palestinian group which runs Gaza, called on Mahmoud Abbas to “retract his decision to participate in the funeral of the criminal Shimon Peres”.
Shimon Peres’ reputation in the region is complicated by the 1996 shelling of Qana in southern Lebanon that killed more than 100 people who were sheltering in a UN compound.
It happened when, as prime minister, Shimon Peres ordered an offensive against a wave of rocket fire by the militant Hezbollah movement.
He later said it was a “bitter surprise” to find that several hundred people were in the camp at the time.
Shimon Peres’ coffin was earlier escorted by a military honor guard from the parliament building in Jerusalem to Mount Herzl, Israel’s national cemetery, where he will be laid to rest alongside many of the country’s former leaders.
Jordan and Egypt – the only two Arab countries to have signed peace deals with Israel – have both sent official representatives to the ceremony.
President Barack Obama is due to speak at the ceremony, along with Shimon Peres’ three children.
Shimon Peres’ body has been lying in state outside parliament in Jerusalem.
Israeli police say 8,000 officers have been deployed for the security operation as thousands of people are expected to attend the funeral.
Police chief Roni Alsheikh said it was “an operation on an unprecedented scale”.
The funeral is expected to be the largest such event in Israel since the funeral of PM Yitzhak Rabin, who was assassinated by a Jewish nationalist in 1995.
Shimon Peres suffered a stroke two weeks ago and died in a hospital near Tel Aviv.
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