The Left party said Prime Minister Narendra Modi's three-day visit to Israel marked a "rupture" in India's long-held position that views that country as an "occupying power" of Palestinian territories.
It alleged the BJP-led NDA government's "alliance" with Israel is a reflection of its "pro-imperialist Hindutva- oriented" foreign policy.
The CPI(M) said it is the "anti-Muslim" bias of the RSS- BJP that makes them emulate Israel, something, it added, the late Hindu Mahasabha leader V D Savarkar had also advocated in 1952.
"The CPI(M) demands that all security and military cooperation with Israel be ended forthwith," the party politburo said.
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Former CPI(M) general secretary Prakash Karat observed that the Hindutva outlook of the BJP has a close affinity with the ethno-nationalist stream of Zionism.
Zionism is a movement that was originally aimed at re- establishing and developing a Jewish nation which is the present-day Israel.
Karat also said Israel's ruling right-wing Likud party and its Prime Minister Benjamin Netanyahu are "ideological soul-mates" of the BJP and Modi respectively.
The Marxist leader made the remarks in the editorial of the forthcoming issue of CPI(M) mouthpiece 'People's Democracy'.
India and Israel yesterday elevated their ties to the strategic partnership level, vowing to do "much more together" to combat growing radicalisation and terrorism while pitching for strong action against those financing and providing sanctuaries to terror groups.