The outspoken Iranian leader raised hackles in Israel on Monday when he said Israelis had been occupying their territory for no more than 70 years. "They have no roots there in history," he added during a visit to New York.
Meeting a group of children in Jerusalem, 89-year-old Peres said Ahmadinejad should have known better.
"It was an embarrassing speech which showed a deep historical ignorance with regard to the deep historical connection between the Jewish people and the land of Israel," he said, adding that Ahmadinejad did not even know the history of his Persian ancestors.
The name Israel first appeared at the end of the late Bronze Age and Israelite tribes were living in the area more than 3,000 years ago, archaeologists say.
Shortly after 600 B.C., Babylonian forces swept through the lands and forced Jews into exile and captivity. But in 538 B.C. the Persians in turn conquered Babylon and King Cyrus let the Jews return to their old homeland.
"Around 2,500 years ago King Cyrus, the King of Persia, granted the Jewish people led by Ezra and Nechamia the right to return to Israel and to rebuild their home. The Jews lived on the land of Israel for thousands of years and there is no lie or leader that can remove chapters of history," Peres said.
Israel is at loggerheads with Iran over its disputed nuclear programme, saying that if Tehran develops an atomic bomb it might use it to try to destroy the Jewish state. Tehran says its nuclear industry is for purely civilian purposes.
(Reporting by Crispian Balmer; Editing by Pravin Char)