Israel's Ministry of Strategic Affairs said the Palestinian-led movement that promotes boycotts against Israel is behind the effort.
Twitter confirmed it suspended "a small network of accounts" in response to the Israeli complaint.
The BDS movement calls for boycotts, divestment and sanctions against Israel in what it says is a nonviolent campaign against Israeli occupation.
The movement has had some success in persuading artists to cancel appearances in Israel and has urged contestants to skip this month's Eurovision. Israel is hosting the contest after Israeli singer Netta Barzilai won last year.
Israeli government minister Gilad Erdan said BDS activists "are trying every deceptive method to attack Israel."
Alia Malak, a member of the BDS campaign's steering committee, accused Erdan's ministry of "desperately spreading propaganda lies to cover up Israel's multiple Eurovision failures."