This weekend's season-opening Australian Grand Prix is not under threat but concerns are mounting over whether next month's Bahrain and Saudi Arabia races will be able to go ahead.
Mohammed Ben Sulayem, president of F1's governing body, the FIA, said in a social media post on Monday that developments were being watched carefully.
He said: "We are in close contact with our member clubs, championship promoters, teams and colleagues on the ground as we monitor developments carefully and responsibly.
"Safety and wellbeing will guide our decisions as we assess the forthcoming events scheduled there for the World Endurance Championship and the Formula One World Championship."
The Endurance Championship is a leading sportscar event due to open its season in Qatar at the end of March.
England Lions have cancelled the remainder of their cricket tour matches against Pakistan Shaheens in Abu Dhabi.
The England and Wales Cricket Board announced on Saturday that the Lions' second 50-over match against the Shaheens in Abu Dhabi on Sunday had been cancelled and they have now abandoned the rest of the tour.
England Women's scheduled training camp in Abu Dhabi ahead of this summer's T20 World Cup has also been scrapped.
West Indies and Zimbabwe have been forced to delay their return from India after their exits from the T20 World Cup due to international airspace closures.
Former US Open tennis champion Daniil Medvedev has indicated he's one of what the ATP Tour calls "a small number of players and team members" they are trying to help leave Dubai.
Medvedev's Instagram account reposted on Monday a report from a Russian-language tennis outlet, Bolshe, which said he was safe and staying at a friend's apartment in Dubai, amid flight cancellations after winning the ATP event there last week.
"The health, safety and wellbeing of our players, staff and tournament personnel is our priority. We can confirm that a small number of players and team members remain in Dubai following the conclusion of the recent ATP 500 event," the ATP Tour said.
Medvedev and others are due to play at the BNP Paribas Open at Indian Wells, California, where main-draw matches start on Wednesday.
Soccer's 'Finalissima' match between Spain and Argentina in Doha on March 27 is in doubt after the Qatar Football Association suspended all tournaments indefinitely.
Euroleague Basketball have cancelled the NextGen EuroLeague qualifying tournament in Abu Dhabi, and basketball's world governing body, FIBA, have called off four games in Beirut and Doha ahead of the second window of the 2027 World Cup Asian Qualifiers.
With agencies
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