Emirates, Dubai's state-owned flagship airline, and sister carrier flydubai resumed check-ins after telling passengers to stay away on Wednesday, when thousands of stranded passengers clogged the airport.

Some 1,244 flights were cancelled and 41 diverted on Tuesday and Wednesday, after torrential rains flooded the Middle East financial centre including its runways and highways.

Traffic congestion remained severe on Thursday, two days after the storms, with at least one major highway completely blocked by water and multiple other junctions and routes also cut off by flooding.

Dubai airport, which carries more international passengers than any other, has witnessed chaotic scenes with thousands of marooned travellers clamouring for information about their flights.

Dubai Airports warned of a "high volume" of people at Terminal 3, which serves Emirates and flydubai, and urged passengers to stay away unless their departure was confirmed.

"There may still be delays to arriving and departing flights," an Emirates statement said, warning that the "airport remains congested".

"Our teams are working hard to restore our scheduled operations as soon as possible," it added.

Nearly 200 departures were listed as delayed or cancelled on Dubai airport's website on Thursday.

Many passengers, unable to take their flights or leave the airport on the flooded roads, have been forced to sleep at the airport, which has been badly understaffed with workers unable to arrive.

One elderly couple's 14-hour flight from Brisbane took 24 hours on Tuesday after it was diverted, and they were then unable to reach their hotel because of the flooding.

"It's just the start of our holiday and I feel like going home -- and I don't know how to do that either," Julie, 72, told AFP through tears, as she tried to navigate the partly suspended metro system to reach her hotel.

"When they landed the plane on this airfield that was deserted, there was no terminal, there were no other planes and I thought we had been hijacked by terrorists," she added, without giving her surname.