More than 7,500 flights have now been cancelled since Friday and over the Christmas weekend, according to the FlightAware data tracking website.
Chinese and US airlines appear to be the hardest hit, with further delays and cancellations announced for Monday.
Companies say the cancellations are due to airline crews testing positive.
Staff who have not tested positive but have been in contact with those infected are then being forced to self-isolate.
Recorded Covid cases are rising sharply around the world, largely driven by the Omicron variant.
Despite early findings that Omicron is milder than other coronavirus variants, scientists are concerned by the sheer number of infections being recorded.
On Sunday, more than 2,400 flights were cancelled - over 800 of which were to or from US airports, according to FlightAware.
The worst-hit US companies are Delta, United and JetBlue.
United warned earlier that a spike in Omicron cases had "had a direct impact on our flight crews and the people who run our operation", adding that it was contacting impacted passengers in advance of them coming to the airport.
Omicron now is the dominant strain in the US.
However, the most affected single airline appears to be China Eastern with more than 390 scrapped flights on Sunday.
The airport in the northern Chinese city of Xi'an has reported more than 120 flight cancellations.
More than 13 million people in Xi'an have been recently ordered to stay at home as authorities attempt to tackle a Covid outbreak there.
Heathrow Airport in London has seen more than 60 flights cancelled on Sunday.
Nearly 5.4 million people have died with coronavirus worldwide, according to America's Johns Hopkins University. There have been more than 279 million confirmed cases.
