GERMAN police have said a hostage situation that shut down Hamburg airport is over, with a man arrested and his daughter safe.

Police previously advised travellers on Sunday not to use Hamburg airport where an armed man is reported to be holding his four-year-old daughter hostage.

The airport, in the northern part of the city, has been closed to passengers and flights since Saturday night when the man broke through a gate with his vehicle, threw Molotov cocktails onto the runway, and fired a weapon twice into the air, according to German news agency dpa.

The situation had been ongoing for more than 12 hours with German officials warning that the airport would remain closed for takeoffs and landing as negotiations with the 35-year-old continued. 

Authorities believe the act had been sparked over a "custody dispute" and said the man’s wife had previously contacted them about a child abduction.

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Police said the 35-year-old man had his four-year-old daughter inside the car after reportedly taking her from her mother by force in a possible custody battle.

A psychologist had been negotiating with the man for hours and there was no indication that other people could be harmed because the airport has been evacuated of all passengers, police said.

“We must currently assume that he is in possession of a live firearm and possibly also explosive devices of an unknown type,” police wrote on X, formerly known as Twitter.

“Our top priority is to protect the child. According to our current knowledge, the child is physically well,” they added.

The mother of the abducted girl arrived at the airport on Sunday and was receiving psychological support, German news agency dpa reported.

“The mother naturally wants to get to her child as quickly as possible,” Malte Stueben, the head of the German Red Cross crisis intervention team in Hamburg, told dpa.

A paediatrician also arrived at the airport to look after the girl once the hostage-taking is over, the news agency reported.

Hundreds of people whose flights could not depart on Saturday night because of the situation were put up at hotels nearby.

Arriving planes were either re-routed to other German airports or cancelled.