The volunteer group - officially known as Syria Civil Defense - was formed in 2013.
The evacuation was carried out amid an offensive by the Russian-backed Damascus regime to retake rebel-held areas in the south of the country, which Israel said presented an "immediate threat" to the lives of rescue workers.
The step would "help solve the refugees' crisis in Lebanon and put an end to their suffering and its social and economic repercussions on the host countries, mainly Lebanon", it said in English.
Netanyahu has also pledged to keep Iran from entrenching itself militarily in neighbouring Syria, where Tehran is supporting President Bashar al-Assad in his country's civil war.
Israel had previously turned down a proposal by Russian Federation, the big-power backer of Syrian President Bashar al-Assad, that Iranian forces be kept 80 km from the frontier, according to Israeli officials.
An operation to evacuate hundreds of rescue workers from war-torn Syria has been condemned as "criminal" by the country's government. "The fact that some White Helmets members left and some stayed hurt us more than it helped us", he tells AFP.
The Syrian government, backed by its ally Russian Federation have seized back control of much of southwest Syria, the area where the insurgency against President Assad first began in 2011.
Euronews has contacted the White Helmets for comment on the reports.
Israel seized 1,200 square kilometres of the Golan from Syria in the 1967 Six Day war, in a move never recognised by the global community.
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"There are no homes, people were staying in tents, and they were lucky if they found tents", another Humanitarian aid worker interviewed by the Guardian said.
Syrian civilians began flocking to the Israeli and Jordanian borders as the fighting intensified, leading to the displacement of more than 320,000 people since June 19, the United Nations says.
A Jordanian government source said 422 people were brought from Syria, over the Israeli-occupied Golan Heights frontier and into Jordan, down from a figure of 800 announced earlier by the foreign ministry in Amman.
The official said the evacuation demonstrated the involvement of Israel, the United States and other western allies in supporting the White Helmets. The group is funded in part by the British government.
The transferred Syrians will remain in a restricted area in Jordan for the time being, Jordanian Ministry of Foreign Affairs spokesman Mohammad al-Kayed told the Jordanian state-run Petra news agency, before onward transfer to Britain, Germany and Canada within the next three months.
Canada has offered to accept dozens of White Helmets and their families from Syria following a dramatic rescue over the weekend that was orchestrated by the Israeli military and personally encouraged by Prime Minister Justin Trudeau.
The Syrian government is unlikely to fire there or carry out airstrikes for fear of an Israeli response.
German weekly magazine Bild, the first to break the news of the evacuation, quoted German Foreign Minister Heiko Maas as saying: "Humanity dictates that many of these fearless first-aiders should now find protection and refuge, some of them in Germany".