Netanyahu also called on Western powers to take the same approach toward preventing "terrorist states" from acquiring nuclear weapons, referring to Israel's main enemy Iran.
"The important international message that came from the attack was zero tolerance for the use of non-conventional weapons," Netanyahu said at the start of a cabinet meeting, describing his discussion with May.
"I added that this policy needs to also be expressed in preventing terrorist states and groups from having nuclear abilities."
Netanyahu also again warned over Iran's presence in Syria after previously pledging not to allow the country to entrench itself militarily next door.
On April 9, seven Iranian personnel were among 14 people killed in an early-morning strike on the T-4 airbase in Syria, with regime allies Iran and Russia blaming Israel for the attack. Israel has neither confirmed nor denied responsibility.
Netanyahu said he told May that Syrian President Bashar al-Assad "must understand that when he allows Iran and its proxies to establish a military presence in his country, he endangers Syria as well as the stability of the region".
Also today, two Israeli ministers said their country would continue to act to prevent Iran from establishing itself militarily in Syria.
Israel has sought to avoid direct involvement in Syria's civil war, but acknowledges carrying out dozens of air strikes there to stop what it says are advanced arms deliveries to Lebanese Shiite group Hezbollah, another of its enemies.
Hezbollah, like Iran and Russia, is backing Assad in the war.
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