A controversial drop-off facility for unwanted babies at a hospital in southern Japan had been open barely three hours before a boy was abandoned there by his father, reports said today.

The boy, believed to be aged three, was left at the 24-hour "stork's cradle" baby hatch at the Catholic-run Jikei hospital in Kumamoto last Thursday.

The hospital, citing privacy, refused to confirm or deny the report but police said they had been notified of one arrival at the hatch, which is heated and fitted with an alarm to alert nurses.

The boy, who has not been publicly identified, was reported to be in good health and told hospital staff his name and that he had travelled to the city by bullet train with his father.

The hospital went ahead with plans to open Japan's first anonymous drop-off point for babies despite strong opposition from conservative politicians, who said it would encourage irresponsible parenting.

But the hospital said the service was necessary to discourage abortions, which are freely available in Japan, and to help desperate women, following a spate of incidents in which babies were abandoned in public places.

The prime minister, Shinzo Abe, is one of the hatch's most vociferous public critics. "I urge parents who have difficulties rearing their children to go to family guidance centres before deciding to abandon them," he said today.

News that the hatch had been used within hours of opening sparked a new round of criticism from senior government officials.

The health minister, Hakuo Yanagisawa, condemned the service, while the chief cabinet secretary, Yasuhiro Shiozaki, said: "If a child has been left there ... that is something that should never happen. Parents have an obligation to raise their children. We find this extremely regrettable."

The hospital, which modelled the hatch on those already available in Germany, insists it is not making it easy for parents to abandon their children.

A sign has been posted at the entrance giving the telephone numbers of advice services and encouraging parents to think twice. Parents can also talk to staff directly via an intercom and those who change their minds later can still be reunited with their children.

"We'd prefer people to come and talk to us than just drop off their babies," said the hospital's director, Taiji Hasuda. "That will help save both the mother and the baby."