"The consequences are not merely to the Iranian forces there but to the Assad regime as well", he said.
Underscoring Israel's concerns, as Netanyahu touched down in Moscow the Israeli military announced that it had shot down a Syrian military drone that entered Israel's airspace, later confirming it also conducted a series of retaliatory airstrikes in the country.
Hezbollah, a militant organization from Lebanon, is believed to have thousands of fighters in Syria in order to help President Bashar al-Assad retain power.
Israel has launched a campaign against, what it claims, to be Iranian targets in Syria in recent months.
The meeting between Netanyahu and Putin is to be their ninth meeting in the last three years.
Graham seemed to concur with Putin's assessment that the Iranians can't be easily removed at this point, and instead wants to see a strong USA military presence in Syria, too. The heart of the matter is preserving our freedom of action against anyone who acts against us.
Earlier on Wednesday, the Israeli army said the downed drone may have been on an intelligence mission. It has threatened to open fire at any Syrian regime forces that try to deploy in a demilitarized Golan buffer zone set up as part of a 1974 UN-monitored armistice.
But he said Moscow should encourage any Iranian forces in the area to leave.
There were no immediate reports of casualties, it said. Under Assad family rule, Syria held direct negotiations with Israel in the United States in 2000 and indirect talks mediated by Turkey in 2008, discussions predicated on a full or partial return of the Golan.
The drone was identified and tracked by Israel's aerial defense systems and later intercepted by an Apache helicopter around 4 a.m. near the town of Beit She'an in northern Israel, the IDF said.
In the heaviest Israeli firing since the start of the Syrian War, the UK-based Syrian Observatory for Human Rights, said the strikes killed at least 23 military personnel, including Syrians and non-Syrians.