The idea is to help the weakest 15 per cent of pupils to progress by giving them two hours' extra coaching in small groups four days a week.
The pilot phase of the project, which is due to start next January and run until the end of the school year, is likely to be aimed mainly at pupils in towns on the country's periphery and in disadvantaged neighbourhoods.
The cost of the pilot phase will be 140 million shekels (Pounds 28 million). If it is successful and is then fully implemented, the cost will be 400 million shekels (Pounds 80m) a year.
Prime minister Binyamin Netanyahu said the government had decided to allocate the money even though it was under terrible financial pressure because education was the real key to the cultural gap. "We don't want to create two societies in Israel," he said.
But Shai Lachman, the head of the National Parents' Organisation who opposed the project, said: "You can't lengthen the school day without a substantial improvement in the schools' infrastructure and physical conditions." He cited a lack of basic facilities, laboratories, heating and air conditioning in some schools.