Israel's new president visited the site of a 1956 massacre, the first Israeli head of state to do so, as part of his outreach campaign to the country's Arab minority.
47 Arab civilians were shot by Israeli border policemen on the first day of the Israel-Egypt war in 1956.
Rivlin said the massacre was a "sorrowful chapter" in Israeli history, calling it a crime for which Israel has rightfully apologised.
"The State of Israel has recognized the crime committed here," he said at the memorial site.
"I too, am here today to say a terrible crime was done here. An illegal command, over which hangs a dark cloud, was given here. The same terrible dark cloud which was ignored by those who carried out the murder of innocents."
Rivlin is calling for calm in the wake of growing unrest in east Jerusalem and the West Bank. He says Jews and Arabs must draw lessons from the killing.
"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.
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