“We are looking for them across the country and abroad,” a police spokesman told AFP.

“We have placed controls at Italian borders, ports, train stations and airports, and we are broadcasting their picture. But we have found no trace of them so far,” he said.

The mother, Caterina Remhof, 26, and her partner, Sascha Schmidt, 24,

abandoned the children after ordering a pizza at a restaurant in the northern town of Aosta on Sunday, according to police.

The man is not the father of the children, who have been placed under the care of social services. One of the children is just a few months old.

One of the restaurant’s managers, Carmelo Casella, said the couple had ordered a pizza at around 8:30 pm.

“Shortly after 9:00 pm, they told me they were stepping out to smoke a cigarette. I didn’t see them after 15 minutres so I went to get them. But they had disappeared,” Casella told La Stampa newspaper.

“I called the police. The children were calm,” he said.

The couple left their car in front of the restaurant with their identity papers inside the vehicle, police said.