Israel's military said that it had detected "irregular activity" by Iranian forces in Syria.
Syrian activists reported Israeli airstrikes hitting targets near Damascus.
Mrs May reiterated her condemnation of the Iranian attacks and the UK's support for Israel's right to defend itself in a telephone call with Israeli Prime Minister Benjamin Netanyahu.
"The Russians were informed prior to our attack by the established mechanisms that we have", Lieutenant-Colonel Jonathan Conricus told reporters without elaborating.
Robert Fisk, who has repeatedly challenged dominant US media narratives on the Syrian civil war and other Middle East crises, argued in a column for The Independent on Thursday that the "latest overnight Israeli air strikes, supposedly at Iranian forces in Syria after a supposed Iranian rocket attack on Israeli forces in Golan-and it's important to use the "supposed" and not take all this at face value-must have been known to the Americans in advance".
The message on Twitter Thursday, a day after Israel once again struck targets in Syria believed to house Iranian materiel and personnel, was unusual for an Arab leader in its blunt defense of Israel.
Israeli security forces braced themselves for an attack, though the place, time and magnitude was unknown.
"We do not know yet the (Iranian) casualty count", he said.
HOT weekend ahead, with more rain coming next week
High temperatures for the week are expected to continue in the 80s with lows likely to linger in the 70s, the NWS predicts. An isolated storm isn't out of the question toward the afternoon or evening, but the rain threat appears low for now.
Amid rising tensions between Israel and Iran, a return to assassinations and overseas attacks can not be ruled out.
The U.S. withdrawal was widely expected to raise tensions between Iran and Israel, which after Trump's announcement placed its military on high alert and deployed more Iron Dome batteries in its northern region.
Israel and Iran have long fought each other through proxies, and with the new exchange each seemed to be sending a warning that a direct clash between them could swiftly escalate. Further waves of missiles followed. It said none of its warplanes was hit.
Iranian forces in Syria have sent rockets hurdling towards army bases in the Golan Heights, across the border in Israel, according to reports. Hours later, state-run Al-Ikhbariya TV broadcast a live feed of Syrian air defenses firing into the sky above the capital, and loud explosions and air defense firing were heard through the night. Israel opened bomb shelters in the Golan Heights, but did not instruct people to enter the shelters. There was no official confirmation. The incoming attack set off air raid sirens in the Israeli-controlled Golan, which was captured from Syria in the 1967 Mideast war. The Syrians fired dozens of antiaircraft missiles at the Israeli jets but did not hit any of them.
Israel describes Iran as its biggest threat and Hezbollah as the biggest threat on its borders.
The official went on to assert that there was "no Iranian military presence, no military bases in Syria".
Trump said he was reimposing economic sanctions on Iran and pulling the USA out of the 2015 worldwide agreement aimed at stopping Tehran from obtaining a nuclear bomb.
Israeli Defence Minister Avigdor Lieberman said the Iranian rockets either fell short of their targets - military bases in the Israeli-occupied Golan Heights - or were intercepted.