Nourine was set to face Sudanese judoka Mohamed Abdalrasool on Monday for his first bout, and would have taken on Israeli Tohar Butbul in the next round.
Speaking to an Algerian television station late Thursday, Nourine said his political support for the Palestinian cause made it impossible for him to compete against an Israeli.
"We worked a lot to reach the Olympics… but the Palestinian cause is bigger than all of this," he said, adding that his decision was "final".
It is not the first time that Nourine has withdrawn from competition to avoid facing an Israeli opponent, after he pulled out of the 2019 world championships in Tokyo.
Iranian judokas have also come under fire for refusing to compete against their Israeli counterparts.