The last news of Quirico, a war reporter for La Stampa, was via a phone call to his wife in early June, in which he indicated that he was alive and still in Syria.
Quirico arrived in Syria on 6th April, and was in touch for a few days, but lost contact from 9th April.
The 62-year-old has a long experience in conflict zones, having covered stories in Libya, Sudan and Mali.
La Stampa initially did not announce his disappearance, saying it wanted to "avoid attracting attention to Domenico in a zone with a high risk of kidnapping."
On Monday, Italian Foreign Minister Emma Bonino reaffirmed the government's commitment to finding Quirico.
"I want to tell Quirico and his family that we are not giving up," she said.
In his speech at the Presidential Palace in Rome on Wednesday morning, Napolitano also called on Italy's coalition government to "stand strong" against the country's recent setbacks, such as the racist slur against Italy's first black minister, Cecile Kyenge, by right-winger Roberto Calderoli earlier this week.
He said that Italy had experienced one of it most "restless" periods over the past year and that the government must not lose sight of addressing the most crucial issue: the country's economic crisis.