According to the Jerusalem District Court, the case is expected to be heard later Wednesday.
The gas platform's shareholders reject the communities' accusations, saying in a statement that gas production is not expected to expose the coastline to environmental damage. The competent authorities have also confirmed this to be the case, according to the statement.
Israeli Energy Minister Yuval Steinitz had first authorized the export of gas to Egypt on Monday.
"Israel, for the first time in its history, is becoming an energy exporter," Steinitz said, according to a statement from his office.
The authorization was for a maximum export of 60 billion cubic metres from Leviathan and 25 billion cubic metres from the Tamar gas field for a period of 15 years, the statement said.
The actual export is expected to begin within two weeks, almost a decade after the discovery of Leviathan, Israel's biggest gas field.
Leviathan lies about 130 kilometres west of the northern Israeli port of Haifa, at a depth of 1,700 metres. Its gas reserves are estimated at around 605 billion cubic metres.
Tamar, smaller than Leviathan, became operative in 2013.
US company Noble Energy and Israeli gas company Delek Drilling are exporting the gas to Egyptian company Dolphinus.
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