Although meetings are scheduled for this week - including a Sporting Working Committee gathering on Wednesday - to try to find a way forward for the sport, Whitmarsh believes that action is needed even before that.
"We clearly have a serious situation where we have to act responsibly, and respect Pirelli," said Whitmarsh, who saw his driver Sergio Perez suffer two tyre failures at Silverstone.
"They have to do the best they can. We have to make a decision urgently, as it gives you a much better chance than talking about it on Wednesday when you want to drive out of the garage Friday."
Whitmarsh claimed that the only solution that would guarantee no repeat of the dramas for next weekend's German Grand Prix was to revert to last year's tyres.
"In 2012 we were not having this problem," he said. "Therefore, if that is a known, established, durable specification, you would have thought that is the easiest thing to do."
Red Bull boss Christian Horner backed Whitmarsh's view that the best short-term solution was to go back to last year's specification.
"The most logical thing would be to go back to the tyres that worked well for them previously," he explained. "The tyres they had last year did not have these failures.
"They need to find a solution, and they need to address it. Whether they go back to last year's car or a different tyre they need a solution."
Lotus team principal Eric Boullier added: "Going back to the Kevlar belt from last year would be one solution.
"I don't know what they have in stock and how quick they can produce tyres. That is a question for Pirelli.
"It is a different track lay-out next weekend and first we need to find out what is causing these failures. But it is a concern."
FINAL ANSWER DOWN TO PIRELLI
Whitmarsh admitted, however, that the final answer would have to be left to Pirelli - as only it had the facts about what went wrong at Silverstone and what tyres it could bring to the Nurburgring.
"I don't think Formula 1 can possibly not respond to the events of this weekend," he said.
"I think there is an argument that the Nurburgring is a slightly less severe circuit than Silverstone, but we have Spa looming not long after that - and we would certainly not want to go there with these tyres.
"But we have to do what is practical. The schedule is tight and we have to work to support Pirelli."
When asked if there was even an argument for the German GP to be cancelled because of the tyre issue, Whitmarsh said: "If they have got sufficient quantities of the 2012 tyres then I have no doubt we go ahead with that as I sense that is a very safe thing to do.
"In fairness to Pirelli I don't know how they can respond in such short order but we have to do what we can to support them.
"We don't want an Indianapolis, but cancelling a race is a big step. We don't have all the technical insight Pirelli have. All I would ask is they do everything they can to give us the most durable tyres they can for next weekend."
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