Renzi, who is in the US this week, said that Italy's involvement in the international coalition, which includes France, Qatar, the United Arab Emirates, Saudi Arabia, Bahrain and Jordan, was in line with United Nations principles and had the support of parliament.
He was speaking at the UN's headquarters in New York as part of a visit this week to the US.
Italy's Foreign Minister Federica Mogherini said last week that the country will send arms and aid to Iraq to fight the militant group but will not take part in air strikes.
A video of the beheading of Hervé Gourdel, 55, a photographer and mountain guide, was posted online on Wednesday, alongside a message from Jund al-Khilafa, a group linked to Isis, saying his killing was in revenge for French involvement in the the "aggresssion against the caliphate." Gourdel was reportedly kidnapped on Sunday after the group tracked his movements on his Facebook page.
The military campaign on Wednesday targetted Isis positions in eastern Syria. A 19-year-old British jihadi is believed to be among those killed by the strikes in the last couple of days.