The Briton's seat at the team has come under increasing scrutiny this season - and while Abiteboul says such pressure is part of life as an F1 driver, he says Renault must help to shield Palmer from the spotlight and allow him to focus on making progress on track. Palmer is yet to score points this year - while new team mate Nico Hulkenberg has picked up 18 points, with four top 10 finishes in the last five Grands Prix.
"Our situation is very clear: [Palmer] has a contract with us; we are completely committed to helping him get through the period," Abiteboul said. "[It] is a tough period, that's obvious.
"He has no ultimatum, but having said that he has to deliver, like every single member of the team. But I think what will help him is that frankly we take him out of the spotlight under which he is constantly.
"That's part of the job, part of the pressure that every Formula One driver has to go through. He has to live with that. We are trying our best to protect him but at the same time to do the best as a team to explain to him what we are expecting and we had that type of conversation with him yesterday – go through the metrics and try to define the targets short to medium terms so that he can improve."
Abiteboul said it would be unfair to pile added pressure on after Palmer's crash in FP2 in Baku, adding: "Today we saw a lot of drivers going a bit outside of the track – a lot, and I mean a lot.
"Clearly, indeed, Jo has been one of those at a Turn that unfortunately doesn't forgive, unlike other turns. Which means there is a bit of damage on the car but it's not huge. Not really different to what Checo did this morning. I think it's a bit unfair to link today and the future."
Abiteboul also scotched recent media speculation that Renault could be eyeing FP1 outings for Robert Kubica later this year, following the Pole's recent test in Valencia.
"Absolutely not," he said when asked if Kubica could be given weekend outings as early as Monza this year. "I don't know where this is coming from and I can completely wipe that one out.
"Robert has been a family member of the Enstone team - [he] made a huge impression on people who've been around, Alan Permane, Bob Bell, Ricardo on the Viry side. People feel very loyal and feel they owe something to Robert for making something big in their life and there was this opportunity that we give to him, that we could afford to him to drive again, because it was actually a marketing event that got cancelled, so we had a car available at the track and we offered that opportunity to him.
"Robert is going through some form of programme to try to understand what he can do. He has been driving a number of cars, Formula E, GP3, F2, LMP2, you name it, so I think he wants to understand what he can do as part of his sort of rehabilitation programme. We'll see. There is nothing else that is planned for the time being."