Marko's future was the subject of speculation on Friday following reports that suggested the 80-year-old Austrian may have been the source of leaks to news media about complaints by a female team member about the conduct of team chief Christian Horner.
Mark held talks in Jeddah with Oliver Mintzlaff, chief executive of Red Bull's parent company ahead of the Saudi Arabian Grand Prix.
The news was welcomed by Red Bull three-time world champion Max Verstappen who expressed his satisfaction as he went to the grid before the race.
After an internal investigation led by an independent lawyer, Horner was cleared of all accusations of inappropriate and controlling behaviour made against him.
"We (he and Horner) have worked together for 19 years, but things have to be solved," Marko told reporters in the paddock before the race.
"We have had a very good meeting and I think everything is clear.
"We had a discussion after these rumours were spread out and there was no legal background. If someone has this wish or idea (to suspend me), it has no legal basis.
"Our goal is to win the championship for the fourth time with Max and for that we all have to work together.”
Flanked by Mintzlaff, he added that he was grateful for the unequivocal support he received late Friday from Verstappen.
"Toto Wolff says contracts don't mean a lot in Formula One and I was really thankful at how loyal he (Verstappen) is and I can only say that I was impressed and thankful."
Verstappen’s veiled threat that he might leave the team if Marko was forced out appeared to have resolved the situation for the troubled Red Bull team.
Asked about Verstappen's future with Red Bull, Mintzlaff made clear he would be staying to complete his contract which runs to 2028.
"Of course," he said. "He has a contract. Max is a great driver and hopefully we will win tonight. I am here just for racing. That’s it."
Horner’s accuser was suspended earlier this week as a direct result of Red Bull's inquiry, which exonerated the 50-year-old team principal.
