The British driver is yet to score a single point versus teammate Nico Hulkenberg's 18 so far, amid rumours he could be ousted mid-season.
"Jolyon must deliver," boss Abiteboul told the French broadcaster Canal Plus.
"He has a contract for the year, now he has to deliver like everyone else," he added.
"The obligation was first on the team -- we had to give him a car that runs well to allow him enough kilometres to do a good job on the weekend, which we did.
"There was really our priority to have reliability, which was putting pressure on us. We put pressure on him as well but it must be positive.
"So I will not start making threats on a driver who does not need that at this stage," Abiteboul said.
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