In an interview with the team's in-house magazine last month, the Red Bull advisor questioned Webber's mental strength, suggesting the Australian cracks under pressure.
Webber responded in kind by claiming the Austrian has his own agenda, the inference being Marko has sided with reigning triple world champion Sebastian Vettel for a long time.
Despite Vettel emerging as champion in the last three years, Webber is in no doubt he can still challenge the German, and at the age of 35 - as he will be later this year - take over the crown.
"I do believe I can have a crack at the championship again this year, as I have done in previous seasons," said Webber on Sunday at the launch of the team's latest challenger, the RB9.
"That is my goal and what I think about each day when I get up, and I'm working hard with the team on doing that.
"They know I need 100 per cent support. You cannot win a world title with only 90, you need 100, and we're going into 2013 with this in place, and I'm comfortable with that."
Team principal Christian Horner was again forced to reiterate Webber is given equal support and the same package as Vettel, and that there is no favouritism towards the 25-year-old.
"Helmut can be outspoken at times," said Horner.
"But if we weren't happy with Mark then we would never have signed him to be with the team for this year.
"We're very happy with Mark and we give both drivers equal opportunity. It's ultimately down to what they do on the circuit.
"Certainly, within the team, that very much is the opinion, approach, and we will continue to do that.
"For us, it doesn't matter which driver wins, as long as it is a driver in one of our cars.
"Both of these guys believe they are the best, and the team will do the very best it can to support them."
There were no surprises when the car was unveiled at a warehouse a short walk from the team's factory, certainly given the stability in the regulations from last year through to this.
As technical guru Adrian Newey remarked: "We've been refining the RB8, so it is an evolution of last year's car.
"With this car, the devil is very much in the detail."
It is why Vettel will start the season as favourite to make it four in a row and continue his current domination of the sport, not that he is promising anything.
"It looks nice, but whether it's quick enough we'll see, and then it's up to us to make it reliable," said Vettel.
"I don't expect any miracles, but I do expect a very long, very tough season with close racing.
"Hopefully we can say at the end of the year we achieved our plan."
That plan was defined by Horner, who added: "There's a fierce determination to keep both of those trophies in the cabinet at Milton Keynes for another year."