The Bahrain and Vietnam Grands Prix have been called off because of the coronavirus pandemic, as Formula 1 expect the season to begin in May.
The Bahrain race was due to be held behind closed doors on 22 March, with the Vietnam Grand Prix on 5 April.
The Australian and Chinese Grands Prix were already cancelled, with the Dutch Grand Prix scheduled for 3 May.
Organisers will assess the "viability of potential alternative dates" later this year should the situation improve.
"Formula 1, the FIA and the promoters have taken these decisions in order to ensure the health and safety of the travelling staff, championship participants and fans, which remains our primary concern," said a joint statement from F1 and governing body the FIA.
It added: "As a result, Formula 1 and the FIA expect to begin the Championship in Europe at the end of May but given the sharp increase in Covid-19 cases in Europe in recent days, this will be regularly reviewed."
The statement suggested the F1 season could begin at the end of May, which means the Dutch (May 3), Spanish (May 10) and Monaco (May 24) Grands Prix could also be in doubt. After that, 15 races are scheduled in the season.
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Seven were cleared on Thursday but an eighth, from McLaren, tested positive.
Vietnam Grand Prix organisers appear to have acted after the government in Hanoi banned travel into the country for anyone who has been in Italy - among other locations - in the previous 14 days.
The Chinese Grand Prix, scheduled to be the fourth race, was postponed in February after government officials said it could not go ahead.
The decisions come on a day of widespread sporting postponements worldwide.
- All elite British football has been suspended until 3 April.
- The London Marathon has been moved from 26 April to 4 October, with the Manchester and Brighton Marathons also postponed.
- Uefa has postponed next week's Champions League and Europa League fixtures.
- In rugby union, Saturday's Six Nations match between Wales and Scotland has been postponed, as has Sunday's Premiership Cup final between Sale and Harlequins.
- Cycling's Giro d'Italia, scheduled to start in Hungary in May, has been called off.
- England's Test cricket series in Sri Lanka has been cancelled.
- Golf's opening major of the year, the Masters, has been postponed.
- Formula 1 has called off the Vietnam Grand Prix on 5 April.
- Formula E is suspended for two months, affecting races in Paris, Seoul and Jakarta.
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