Fire Department vehicles arrive at a security scene at the Hamburg Airport in Hamburg, Germany, on Saturday. AP

Hamburg airport remained closed on Sunday, authorities said, as police dealt with a hostage situation they say likely involves a custody dispute.

The airport closed for all takeoffs and landings on Saturday evening after police arrived in large numbers on the scene to deal with a man who drove through a barrier onto the grounds of the airport with a child.

The car with the 35-year-old man and 4-year-old child was parked under a plane, a police spokesperson said.

"The operation continues. Our negotiators are in contact with the person in the car," the police posted on Sunday on the social media platform X, formerly known as Twitter.

Police said the child's mother had told them the father had been in contact with her.

Police would not confirm their earlier statements that the man was armed and had fired shots.

According to another report, traffic at Hamburg airport was halted and the terminals evacuated on Saturday night over a "hostage situation" believed to have arisen over a custody dispute, police said.

Police guard the scene of a security breach at the Hamburg Airport in Hamburg, Germany, on Saturday. AP

At around 8 pm (0600 GMT), a gunman had rammed his car through the security area onto the tarmac, firing two shots in the air and flinging two burning bottles out of the vehicle, a police spokesman said.

At least two individuals — including a child — were in the car, police said.

The wife of the driver had placed an emergency call alerting police to the abduction of her child, the spokesman added.

"We are on site with a large contingent of emergency services. We are currently assuming a static hostage situation," Hamburg police said on X, formerly known as Twitter.

The car remained parked in the apron area of the airport.

Police vehicles and ambulances arrive at a shooting scene at the Hamburg Airport. AP

Police added later Saturday that they believed "that a custody dispute is the background to this operation".

Psychologists as well as officers specialised in negotiations are on site, said police, adding that they were in contact with the individual in the vehicle.