PARIS — France confirmed a second case of a new coronavirus belonging to the same family as SARS on Monday, saying a man who shared a hospital room with the first victim had been infected.

The announcement came a day after the World Health Organization announced that the new virus seemed capable of passing between humans, but only after prolonged contact.

The organization is carefully monitoring the virus, which was first identified in the Middle East in September and has killed more than half of the 34 people believed to have been infected. On Sunday, an assistant director-general at the World Health Organization, Dr. Keiji Fukuda, said there was no evidence so far that the virus was able to sustain “generalized transmission in communities,” easing fears of a pandemic.

Dr. Fukuda spoke in Saudi Arabia, the site of the largest number of infections. “The different clusters seen in multiple countries,” he said, seemed to “increasingly support the hypothesis that when there is close contact, this novel coronavirus can transmit from person to person.”