Flavio Briatore, a member of Webber's management team and former F1 team principal, reacted by claiming Webber and Vettel's relationship was beyond repair and that he expected the two "enemies" to be parted at the end of the season.
But Red Bull today insisted it was too soon to speculate on the team's likely line-up for next season.
"It's pure speculation that Mark will not drive with the team in 2014," Red Bull said .
"Mark's contract has been renewed for the last few years on an annual basis - he has continually chosen to drive for the team each year and the team has similarly wanted to continue working with him as he is an excellent driver and a competitive racer.
"We are two races into the current season and it's far too early to be talking about 2014."
The reigning world champion overtook the 36-year-old despite being instructed not to by the team because of the need to look after the tyres and save fuel.
Webber had turned his engine down in response to the orders from the pitfall and was furious with the 25-year-old German for putting himself above the team.
Others, including Briatore, questioned who was really in charge at Red Bull.
The Italian, who was banned from Formula One after the Renault team he led were found to have ordered Brazilian Nelson Piquet junior to crash deliberately to help his team mate Fernando Alonso, accused Horner of weakness in a radio chat show in Italy.
But Red Bull last night hit back, saying: "A 'weak' team principal would be unable to steer a team to three consecutive world championships and oversee and manage the extensive team work that goes into this achievement - while managing two talented racers.
"This feat has only ever been achieved by four teams in the entire history of the sport."
The team added that the pairing of Webber and Vettel had won 35 races, taken 80 podiums and 13 one-two finishes since their first season together in 2009.
"This successful period includes some spells of intense on-track rivalry between the two drivers, which began in Turkey 2010 and has seen both drivers ignoring team orders at different times," it said.
"The team has managed the situation each time in its own way behind closed doors."