
Benitez met with Gillett, co-owner Tom Hicks, Foster Gillett and Rick Parry, the club's chief executive, for three hours on Sunday after the club's 1-0 defeat by Manchester United.
The manager had been upset with the owners for their apparent reluctance to back him in the transfer market when the window reopens next month, while Gillett and Hicks were reportedly upset he aired his grievances in public.
But according to the Liverpool Echo newspaper, in an address to the Liverpool Former Players Association - Gillett said Benitez had the owners' full backing.
"This wasn't supposed to happen, but it has happened, and now the focus has to be on finding a common platform to continue our co-operation," he said.
"Rafa is the one we want as a manager further on, and we have faith in him. I've been married over 40 years and have first-hand knowledge about how to solve an argument.
"We concentrated on getting an overview over the situation, and I felt we accomplished that."
"The transfer window opens soon and we might use the option that gives us, or we might not.
"Liverpool is a great club. We are well aware that we have something very valuable on our hands.
"Liverpool is not our club, it's your club. The supporters' club. It's always been that way, and it will always be that way."
Liverpool are 10 points behind leaders Arsenal, though they do have one game in hand.