Earlier this year Red Bull motorsport advisor Helmut Marko said that Webber had problems dealing with the pressure that came with fighting for the title.
Asked by Gazzetta dello Sport whether that meant Red Bull would put its full weight behind three-time champion Vettel, Mateschitz insisted Webber would have a fair chance.
"I absolutely believe that and I'm certain that it will be so," Mateschitz said.
The Austrian described Webber as 'exceptional'.
"Mark is at the same time a strong and charismatic character and an exceptional racing driver," said Mateschitz.
"It's a fact that competition begins inside your own team. That means that the environment is tough but friendly, and that's how it's supposed to be."
Webber had shrugged off Marko's remarks in an interview on his personal website last month.
"Look, everyone at this level has their own agendas and it's been evident for a long time now that I've never been a part of Marko's," Webber said.