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A Southwest US-bound flight was forced to make an emergency landing after birds struck the plane's engine, the airline said.

The plane - flying from Havana to Fort Lauderdale, Florida - filled with smoke following the collision shortly after take-off on Sunday morning, Southwest said in a statement.

No one was injured in the incident.

The pilots safely returned to Havana where customers evacuated the aircraft via slides, Southwest said.

show passengers on Southwest Airlines Flight 3923 panicking and children crying as smoke filled the cabin and pilots made an emergency landing.

"Nobody could breathe," Marc Antonio, a passenger on the flight told NBC's Early TODAY show. "It was burning so much in the lungs."

"People were just screaming. Kids were screaming," he added.

The Boeing 737 plane was transporting 147 passengers and six staff members, Southwest Airlines said in a statement.

Passengers were in "good condition" after evacuating the plane, the Cuban Aviation Corporation SA (CACSA) told state-run Cuban outlet Radio Rebelde, adding that the event was being investigated.

Travellers were taken to an airport terminal and were expected to be put on a different flight to Florida.

"We apologize to our customers for the inconvenience and have reached out to address their needs and offer support," the airline said.