Rivlin spoke at a memorial ceremony for victims of the 1956 massacre at Kafr Qassem, where Israeli forces killed 47 residents of the central Israeli Arab village for breaking a wartime curfew, becoming the first Israeli president to attend the event.
"A terrible crime was committed here," he said. "The brutal killings in Kafr Qassem are an anomalous and sorrowful chapter in the history of the relations between Arabs and Jews living here.
"I came here today, specifically during these difficult days, to reach out my hand in the belief that your hands are outstretched to me and to the Israeli Jewish public in turn," the president said.
Violence pitting Palestinians against Israeli police has shaken annexed east Jerusalem on an almost daily basis since the murder of a Palestinian teenager by Jewish extremists in July.
Clashes intensified during the 50-day Gaza war over the summer.
Rivlin's visit came as preparations were underway for the funeral of an east Jerusalem man who on Wednesday drove his car at high speed into a crowd of Israelis, killing a baby.
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Kafr Qassem is situated in central Israel, adjacent to the West Bank.
In 1956, it was under military rule, and on October 29 -- the first day of a war with Egypt -- Israeli border policemen gunned down residents who were unaware a curfew that had been imposed, killing men returning from work in the fields as well as women and children.
Arab Israelis number around 1.4 million, some 20 percent of Israel's population.
They are the descendents of 160,000 Palestinian Arabs who remained on their land when the Jewish state was established in 1948.
“I am not naive," Rivlin said. "We belong to two nations, whose dreams and aspirations, to a great extent, contradict each other.
"Many Israeli Arabs, who are part of the Palestinian people, feel the hurt and suffering of their brothers on the other side of the Green Line. Many of them encounter racism and arrogance from Jews," said the Israeli president.
"The Arab population in Israel, and the Arab leaders in Israel, must take a clear stand against violence and terrorism," Rivlin stressed.
The Kafr Qassem massacre is taught in the Israeli education system as a case of an illegal military order that must be refused by soldiers.