Israeli media said that three people were hurt in the clashes on Saturday night, despite a reinforced police guard that barricaded a section of the city after nightfall to contain stone-throwing protesters.
Rosenfeld said that more than 700 officers remained on patrol in the coastal city to try and contain the violence.
Businesses closed
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.
Unrest erupted on Wednesday when an Arab motorist drove into a neighbourhood where Arabs and Jews live, playing his car stereo loudly as ceremonies marking Yom Kippur were under way, Rosenfeld said.
Abbas Zakour, an Arab politician from Acre, said he was trying to mediate a truce under which representatives of Arab residents would condemn the driver involved in the Yom Kippur incident.
"These have been a few difficult days for Jews and Arabs," Zakour said. "We should sit down together. I hope we succeed."
Driver assaulted
A group of Jewish youths assaulted the Arab driver accusing him of deliberately disrupting the sanctity of Yom Kippur, a day when observant Jews are not allowed to drive.
"Rumours then spread out, namely from mosques, claiming that the motorist had been killed, prompting several hundred Arabs to take to the streets," Rosenfeld said.
Football matches planned for the weekend and an annual theatre festival that was scheduled to be held next week were cancelled.
"The atmosphere in the city is not one that is right for a festival," Albert Ben-Shushan, the festival's director, told Israel's Army Radio.
"When it all ends, and fades, and the dust settles, we'll decide."
But some MPs criticised the decision to call off the festival, which brings thousands of visitors to Acre and is a major boost for local businesses.
"It is an expression of co-existence in Acre," Ophir Pinez-Paz, who heads the Knesset's Internal Affairs Committee, said. He insisted that the festival should be held "despite the events and maybe because of them".