Recent four-time constructors champions Red Bull finished a lap down on Lewis Hamilton's Mercedes in the opening race of the 2015 season.
Technical boss Newey stated "we've got an engine which is quite a long way behind".
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But Renault's engine chief said: "It's hard to have a partner who lies."
He added on French site Autohebdo: "Adrian is a charming man and an engineer without equal but he has spent his life criticising engine partners."
Red Bull have been contacted by BBC Sport for a response to Abiteboul's quotes.
The Austrian team dominated Formula 1 for four seasons between 2010 and 2013, winning the constructors' championship while Sebastian Vettel collected successive drivers' championships.
However, that dominance was ended by Mercedes and Lewis Hamilton last year.
Abiteboul added: "In addition to our problems, Red Bull has some chassis problems which don't help the situation.
"In particular, the lack of rear stability. These two problems combine to ensure the car is difficult to drive."
Renault chief Cyril Abiteboul has accused Red Bull's Adrian Newey of lying after he blamed the car's problems on the engine.