Tyre supplier Pirelli, who have faced criticism from some teams since the start of the season, began an immediate investigation after four drivers suffered rear-left tyre failures at Silverstone.
Ferrari's Brazilian Felipe Massa, who was almost killed by debris shed from a car in front of him at the 2009 Hungarian Grand Prix, would not rule out drivers considering a boycott if solutions were not in place for Sunday's race at the Nuerburgring.
"I don't want to say that (drivers would walk out) because I don't want to create loads of problems but this is something that for our safety we can do," he told reporters after he experienced one of the blowouts.
McLaren's Sergio Perez, another victim of the exploding tyres, said drivers were risking their lives and needed assurances.
"If something like this happens again, we don't want one of us to be killed," he said.
Australian Mark Webber, second for Red Bull in the race, said it had been like Russian Roulette and he had been praying for a safety car because nobody knew who would be next.
Perez's team principal Martin Whitmarsh warned that driver action could not be ruled out.
"I think there's that danger (of a boycott) and rightly so," he told Sky Sports television. "If the drivers and the teams can't be convinced that they can do so safely, then they would have to resort to that.
"That's not what we want for Formula One. We've faced some of these issues before. We had it in Indianapolis and that was terrible for the sport," Whitmarsh said, referring to the 2005 US Grand Prix when only six Bridgestone-shod cars started after problems with the Michelin rubber.
"So we've really got to work together. This is not a time to point fingers. It's a time to work together, find the solution, get on with it."
Whitmarsh expected something to change before cars appeared on track again in Germany and McLaren were not considering any drastic action at present.
The immediate question is whether the problem was track specific, with failures caused by debris or a particularly sharp kerb at Silverstone cutting into the tyres, or something related to the construction and design.
Pirelli's motorsport director Paul Hembery said on Sunday that the Italian company had ruled out the cause being linked to a new bonding process introduced ahead of Silverstone.
He will join a meeting on Wednesday of Formula One's sporting working committee, although teams will want to see something tangible before then.
Pirelli had wanted to make more fundamental changes but needed the unanimous agreement of teams and some - notably Ferrari, Lotus and Force India - have objected because their cars are working well with the tyres.
This year's tyres have a high-tensile steel belt under the tread - designed to make it hard for objects to penetrate and cause a sudden deflation - whereas the 2012 versions used a Kevlar belt.
The new bonding process was aimed at preventing embarrassing 'delaminations' experienced at previous races where the tread peeled away when penetrated by debris but the main body of the tyre beneath the belt remained inflated.
Red Bull boss Christian Horner and Whitmarsh both suggested reverting to the harder 2012 tyres for Germany but the calendar is not on Formula One's side and substantial change may have to wait until Hungary at the end of the month.
A stopgap solution might be to impose mandatory tyre pressures but that would be difficult to police, given the competitive advantage at stake.
"If we keep these tyres, we will have a safety issue," said McLaren's Jenson Button, the 2009 world champion. "We were lucky that nothing worse happened.
"Five tyre explosions, whether it is from debris or a tyre failure I don't care. The result is still the same and the danger is the same. The issues are plain to see. We are not going to let that go."