ROME, March 17 (Reuters) - Italy's government is poised to curb the use of Russian anti-virus software in the public sector in the wake of Russia's invasion of Ukraine, fearing Moscow could hijack the programs to hack key websites, officials said.

Franco Gabrielli, the state undersecretary for security, told the Senate on Tuesday that the government was working on rules to allow state bodies to pull the plug on software developed by the Russia-based Kaspersky Lab.

A government source told Reuters that the new rules would let public administrations replace all software deemed potentially dangerous, without facing penalties.

A second source said the regulation could be approved as early as this week.

Kaspersky Lab did not immediately respond to requests for comment on Thursday. But its general manager in Italy, Cesare D'Angelo, told newspaper Corriere della Sera on Wednesday that the company applied the highest standards of quality and transparency.

"We fully understand the doubts of the institutional partners in the light of the ongoing tragedy. We are available to anyone who wants technical clarifications or wants to examine us," he said.

In a recommendation issued on Tuesday, Italy's state cybersecurity agency said there was no evidence products provided by companies linked to Russia had been compromised since the Feb. 24 invasion of Ukraine.

However, it warned that risks needed to be reassessed amid the growing conflict and that anti-virus software was particularly sensitive due to the "high level of invasiveness" of the systems they serve.

Earlier this week, Germany's cyber security agency warned users of the Kaspersky software that it posed a serious risk of a successful hacking attack.

Kaspersky called that announcement political and said it was a privately-managed company with no ties to the Russian government.

In a sign that Italy's business world was also sensitive about its ties with Kaspersky, Formula One team Ferrari said on Thursday its sponsorship deal with the firm had been suspended by mutual agreement. A Ferrari spokesperson also said the company was assessing its use of Kaspersky antivirus software. (Additional reporting by Elvira Pollina and Giulio Piovaccari; Editing by Crispian Balmer and Andrew Heavens)