The Israeli company, which manufactures a device for making fizzy drinks at home, announced in late 2014 it was closing its plant in a West Bank settlement, following a boycott campaign that included targeting Hollywood actress Scarlett Johansson after she advertised its product.
The plant closed in October 2015, with more than 500 Palestinians made redundant, the company said.
They relocated the factory inside Israel, bringing 74 Palestinian workers with them, as well as hiring hundreds of Israeli workers.
"We are not willing to let Israeli bureaucracy determine the future of 74 people," he said, adding many have worked for the company for at least six years.
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"We hope that the current government will be able to solve the bureaucracy that now points to the termination of the contracts of our 74 Palestinian workers," Nave said.
He said the company would consider suspending production at the factory in the Negev region if the government did not meet its demands.
A Palestinian employee quoted in the Israeli media said that, since the factory move, he had to leave his home in the occupied West Bank at 4:30 am and did not return until 7 pm.
"It's a long day and I don't get to see my children during the week, but I'm happy that I have this job," he told The Jerusalem Post, which first reported SodaStream's concerns.
COGAT, the defence ministry body responsible for coordinating Israeli government activity in the Palestinian territories, said it was trying to help the company as much as possible.
According to COGAT, 58,000 Palestinians hold permits to work in Israel, with another 27,000 working for Israeli businesses in West Bank settlements and industrial zones.
Nave called for an increase in the number of permits, but COGAT said it would need a ruling from the government.