"I do believe I can have a crack at the championship again this year, as I have done in previous seasons," said the 36-year-old who has been beaten for the last four years by team mate Sebastian Vettel.
"That is my goal and that's what I'm getting up each day thinking about," he added.
"They know that I need 100 percent support. You cannot fight for world championships with 90. You need 100...we're going in to 2013 with this in place and I'm comfortable with that."
Red Bull advisor Helmut Marko made headlines last month when he said in an interview with Red Bull's own Red Bulletin magazine that while Webber could win races, he struggled to handle the pressure of a championship challenge.
The Austrian, who is close to Webber's German team mate Vettel and to the team's Austrian owner Dietrich Mateschitz, added that Webber fell "easily into a downward spiral" if something went against him and suggested losing a title battle with Vettel in 2010 had been a crushing psychological blow.
Webber subsequently accused Marko of having his own agenda in the team but principal Christian Horner smoothed down the controversy at the launch of the new RB9 race car.
Horner said Red Bull would not have given Webber a one-year contract extension if they had not been happy with his performance.
"As we all know, Helmut can be outspoken at times in some of his comments and that reflected his opinion and sometimes these things can be misinterpreted as well," he said.
"We are very happy with Mark. We give both drivers equal opportunity and it's ultimately down to what they do on the circuit and certainly within the team that very much is the approach.
"We will continue to do that," added Horner. "For us it doesn't matter which driver wins so long as it's a driver in one of these cars...as a team we will do the very best we can to support both drivers."
January's comments by Marko were not the first directed against Webber by the Austrian. A former F1 driver, he blamed Webber in 2010 for a collision with Vettel in Turkey that dumped the German out of the race and denied the Australian, who was leading, the victory.
Webber will be the first to test the new car at the Jerez circuit in Spain on Tuesday.
The Australian expected the 'usual suspects' to be strong but said he had not seen a single picture of any other team's cars so far.
"I focus on this baby," he said, standing next to the RB9.