"I was surprised by the extent of appeals for peaceful co-existence issued by leaders from both sides," Peres said.
"We are destined to live side by side, and a bright future awaits Acre."
Peres was accompanied by Avi Dichter, the interior security minister, and Israel's two chief rabbis, Yona Metzger and Shlomo Amar.
Police said the clashes broke out on Wednesday when an Arab resident drove through a conservative Jewish neighbourhood blaring music from his car stereo.
A group of Jewish youths assaulted the driver, accusing him of deliberately making noise and disrupting the sanctity of Yom Kippur, the Day of Atonement, when most Jews in Israel observe a religious ban on driving.
Hundreds of Arabs then took to the streets, damaging around 100 cars and 40 shops, according to the police.
Ethnic riots
In the ensuing days Jewish and Arab rioters clashed with each other and with police.
Arabs with Israeli citizenship, the descendants of those who remained in Israel after the 1948 war that followed its creation, make up around 20 per cent of the Israeli population.
Police fired water cannons to disperse crowds and arrested 32 people from both sides on Saturday, and three Arab homes were torched and damaged, Micky Rosenfeld, a police spokesman said.
Many shops and restaurants in the old town, a popular tourist destination, were either closed or bereft of any business on Saturday.
The ancient port of Acre is populated by both Jews and Arabs who live in adjacent and some mixed neighbourhoods.