Chris Horner has said that he will dedicate himself to team-mate Rui Costa in the days ahead at the Tour de France, believing that the world champion has a better chance of doing something in the overall than he does.

The American spoke to a cluster of reporters just after the end of stage 13 in Chamrousse and said that both he and Costa are still not quite over the illness which affected them in recent days.

“I wasn’t 100 percent for sure,” he said of the final Hors Categorie climb. “You could see the power was down. But I just…the guys that we were with, the top four or five, you can’t follow, but the other guys I can follow. When they accelerate you have got to let them go.

“I have got Rui with me and for sure he is going to be better than me. We just have to keep it regular. Both him and I have gone through some weird bronchitis or something in the lungs that has been giving us a problem. It was better today, Rui was better, so hopefully it comes good tomorrow.”

Horner rode with Costa on the climb and also did other work during the stage. Both limited their losses to the fastest riders; Costa wheeled in 15th, three minutes and one second behind the stage winner and ongoing yellow jersey Vincenzo Nibali (Astana), while Horner was two places and ten seconds further back.

“I am just trying to minimise the damage,” he said. “If he [Lampre Merida team-mate Costa] comes really good, he is going to be with the best guys up there. I don’t think my form is going to put me with the top three.

“If I ride ninth or tenth or if I am 15th, that is not much of a distance, but if I can save Rui a little bit and his legs keep getting better and better and him and I, if our lungs get better, we are going to be in the front group. So we just got to minimise damage and hopefully the form gets better as we go on.”

Costa is now ninth overall, 8 minutes and 35 seconds behind Nibali. The overall win is likely long gone, but the Tour de Suisse champion is just over four minutes off the podium. If he is indeed stronger in the days ahead, he will push hard to see what is possible.

As for Horner, he’s clearly not at the same level he was when winning last year’s Vuelta a España. He is 15th overall, 11 minutes 11 seconds back, but is willing to keep riding for Costa and perhaps to then try to defend his Vuelta title next month.

While he acknowledged that Nibali was very strong, he said that the battle for the final yellow jersey wasn’t done and dusted.

“You saw that Nibalia was isolated but still nobody has any gas to get away from him,” he said with a laugh. The Tour is not over. He is isolated.

“Who knows – maybe if something happens or his team blows on the second to last climb, maybe there will be some action. They didn’t have to ride at all today. You saw it was Katusha riding almost all day, then on the second to last climb they weren’t really riding that either. We weren’t doing big, big power there.

“So it was really just the last climb where they rode on the front. We will see. Of course Nibali is the best, we all know that, but it is just going to come down to tactics. Or maybe he gets bronchitis too,” he laughed.