"He is alive and well. He called his wife today and spoke to her for a few seconds. He is still in Syria and we hope to see him again soon," wrote La Stampa's editor Mario Calabresi on the microblogging website Twitter.
Calabresi thanked media for respecting a news embargo on 62-year-old Quirico, but warned the reporter was still in danger.
"Italy's foreign ministry asks for caution... the situation remains extremely delicate," Calabresi tweeted, adding he had confidence in the Italian authorities.
In an TV interview on Friday, Italy's defence minister Mario Mauro said confidentiality was vital for Quirico's safe release.
"The highly complex and confused situation on the ground [in Syria] makes it hard to fathom the identity of the possible captors to negotiate with," Mauro told La 7 television channel.
"Discretion is indispensable to achieve a positive outcome," he stressed.
Quirico's two daughters had appealed for his release in a video on 1 June aired by Arab media.
On 3 May, Rome prosecutors opened a kidnapping and anti-terrorism investigation into Qurico's disappearance in Syria on 9 April while travelling to report from the city of Homs after entering the war-wracked country on 6 April.
La Stampa only made Qurico's disappearance public on 29 April.
Fears for Quirico's welfare have been intense. The civil war has made Syria one of the most dangerous countries in the world, including for reporters.
Four Italian journalists were kidnapped in Syria in early April and were released after just over a week in captivity. The civil war has made Syria one of the most dangerous countries in the world, including for reporters.
A seaoned war correspondent, Quricio has reported on conflicts in Sudan, Uganda and Libya and on the Arab spring uprisings.
He was abducted in Lebanon in August 2011 with two colleagues from dailies Corriere della Sea and Avvenire and held hostage for 48 hours before being released.
He had also been known to fall under the radar for a few days at a time war reporting assignments but never for such a long period.