US Secretary of State Antony Blinken is expected to endorse Israel's candidacy for the program on September 27.
In return for visa-free access for Israelis, Washington has demanded that Israel provide reciprocal unfettered passage for Americans, regardless of their background.
Prigozhin flew into exile in Belarus on Tuesday under a deal that ended a mutiny by his fighters.
Interior Minister Moshe Arbel's May 1 passport marathon plan would dedicate four major ministry offices to applications to tackle the passport renewal backlog.
The passing of the bill reverts the country back to a law that existed until 2017.
Interior Minister Moshe Arbel: "The passport marathon operation continues in full force."
2.9 million Israelis, or around 37% of the population will have their ID cards expire in the coming years, Matanyahu Englman said.
Israeli Interior Minister Moshe Arbel called for people to be patient and prepare to wait for hours in lines at the passport offices.
The NGOs called on the Interior Ministry to retract the cancellation of visa services, or reduce the plan to two days a week.
The expectation that citizens should roam the length and breadth of Israel in order to find an appointment slot somewhere in order to renew a passport is preposterous.
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