Marko's future at the F1 squad had been the subject of speculation after it emerged that he was at risk of suspension amid an investigation into the alleged leaking of information surrounding the recent Christian Horner investigation.
Speaking to Austrian television on Friday night, Marko had said there was a chance he could be out of the team after this weekend and not be part of the squad for the next race in Australia.
But, following a meeting with Red Bull CEO Oliver Mintzlaff at the Shangri-La hotel in Jeddah on Saturday morning, it appears that Marko has been assured of his future.
Speaking to Sky Germany about the outcome of those talks, Marko said: "It was a very good conversation. Of course, calm must return to the team. That has priority.
"We agreed on all points. I will continue here. My contract still has three years to run. But calm must return."
The vote of confidence comes after a dramatic 24 hours where Red Bull driver Max Verstappen all but threatened to quit the team if Marko was let go.
Verstappen said that Marko should be respected for all he had achieved at the team, and was critical to his own future at the squad.
Asked about Verstappen's commitment to him, Marko said: "It was very impressive. I am very grateful to him for that. But he is one of the few who has strength of character and shows loyalty."
Marko went on to explain that the claims he had leaked information to the media were totally false, as he fully distanced himself from the anonymous emails released over the Bahrain Grand Prix weekend that contained alleged evidence at the heart of the Horner saga.
"The leaking is complete rubbish," he said. "I'm glad I can manage to use my mobile phone. I've never seen any of these chats."
It is understood that Mintzlaff will travel to Dubai following the Saudi Arabian GP to meet with the Thai majority owners of Red Bull.
Speaking briefly in the paddock in Saudi Arabia, Mintzlaff said: "We are focusing on the racing. We are happy with our management."
