The manufacturer, partner to seven of the 10 teams, said it was baffled by the failures and had sought permission to fly in new tyres of a different specification from their French factory.
Should Michelin be denied the request, while also failing to get to the root of the problem, they said their advice would have to be a withdrawal.
"As it stands today, we would advise the teams that they shouldn't race," Michelin's Formula One head Nick Shorrock said at Indianapolis on Saturday.
"That is unless there is any new information coming through from the tests that are under way.
"If we have no further information on the product that we've got and why we had the failure yesterday, we will not allow the teams to go out and race - or propose to the teams not to go out and race," said Shorrock.
"The final decision is with the teams but our very strong advice, because we have a legal responsibility for our product, is to give them that advice and the arguments necessary to use the product in a safe manner."
Michelin supply championship leaders Renault, rivals McLaren, Williams, Toyota, BAR, Sauber and Red Bull.
Champions Ferrari use Bridgestone.
Toyota's Ralf Schumacher has already been ruled out of Sunday's race after suffering one of two tyre failures in Friday practice. The German crashed into the wall at the quickest part of the circuit, the banked final corner were cars reach speeds of about 300kph.
The rules demand that teams make the same tyres last for qualifying and the race and any change would require a special dispensation. There was no immediate comment from the governing FIA.
"For as long as we can't put our finger on why we had the problem we had yesterday, it would not be responsible of us to allow our drivers to go out and race," said Shorrock. "The initial priority is one of safety for the drivers."
He said teams would use the same tyres in qualifying that they had in Saturday morning practice pending further advice.
Michelin advised teams to change set-up for Saturday's second practice but Shorrock said doubts remained about lasting a full race distance.
McLaren boss Ron Dennis suggested his team, who have led every practice session and won three of the last four races with Finland's Kimi Raikkonen, would be inclined to race.
"We wouldn't endanger a driver's life knowing that there was an unacceptable level of risk, that's a question of risk management," he said.
"Over the last few races we've had problems on our cars and you have to take a view and assess risk and this is no different.
"If I had to decide today, I think my preference would be to deal with what we know."
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