F1 boss Chase Carey insisted Friday it was too soon to say whether other races will be cancelled this season over rising coronavirus fears as McLaren said 15 team members were now in quarantine.
The pin was pulled at the last minute on the opening Grand Prix of the year in Australia as concerns spiked following a McLaren staff member testing positive.
It saw the team withdraw from the Melbourne race and McLaren said another 14 personnel were now in quarantine at the team hotel for two weeks, in accordance with local health authority directives.
They were all in close contact with the person who tested positive.
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"Any other team members who show symptoms will be tested immediately and self-isolate, in line with our protocol," McLaren said.
With so many staff out of action, McLaren's participation in the next race at Bahrain this month, that organisers already said will be run without fans, is in doubt.
Carey refused to be drawn on whether Bahrain and the third Grand Prix in Hanoi would also be called off, insisting it was too early to say given the fluidity of the situation.
The fourth race in China has already been postponed, with Holland scheduled to run after Vietnam.
"Right now, here, we are addressing the issues in Australia. We will in the coming days be looking at races that are more imminent like Bahrain and Vietnam," Carey said in Melbourne.
"And we will have further announcements and decisions on how we navigate the short-term elements of our schedule. We know there are issues there."
Carey, who was in Hanoi for talks about the inaugural Vietnamese race this week, said the situation was changing so rapidly it was hard to predict what might happen.
"It's a pretty difficult situation to predict," he said, describing the situation as "fluid".
"I'll use the last five days and you look at how things have changed over the last five days. Trying to predict what it is going to look like going forward I think is unrealistic."
"Everybody wants an answer, we'd love to have an answer," he added. "I think you can't force an answer right now to something you don't have an answer to."
With the lucrative 22-race calendar under threat, there has been talk about whether cancelled races can be rescheduled for later in the year.
But Carey said there was no point thinking that far ahead.
"I don't think at this point it's productive to get into hypotheticals," he said.
"Longer term we will see where it evolves. Obviously everybody hopes the world will get back to a place where it is a functioning world and functioning marketing places."