Forest rangers on Sunday continued the search for the two cubs of a female bear called Amarena that was shot dead late on Thursday by a man using a rifle on the outskirts of the Abruzzo town of San Benedetto dei Marsi.
It is feared that the cubs will not be able to survive on their own in the wild.
"The situation is not easy," said Luciano Sammarone, the director of the Abruzzo, Lazio and Molise National Park (PNALM).
"They run away (when approached)".
San Benedetto dei Marsi Mayor Antonio Cerasani called on the public not to do anything that might hinder the search for the cubs.
On Saturday the two cubs were spotted together and then one was seen on its own, but efforts to capture them, including using traps, have so far failed.
"It gets more difficult to find the two mammals with every day that passes," said Cerasani.
"I invite everyone to cooperate by not getting in the way of the search and alerting the emergency services to any sightings.
"There is still hope".
Amarena's killing has sparked widespread outrage in Italy.
The PNALM said the it was "unjustified" and had caused huge damage, as it had taken out one of the park's most prolific females ever, stressing that Amarena "had never caused any type of problem to humans".
Abruzzo Governor Marco Marsilio described the killing as "incomprehensible".
The 56-year-old man who killed the animal has been put under investigation.
He said he had reacted instinctively after the animal frightened him by appearing on his property.
Avezzano prosecutors have tasked two experts, a vet and a ballistics specialist, with the job of establishing the dynamics of the episode.
Source: Ansa News Agency (ANA)