Foreign ministry director general Yuval Rotem spoke with ambassador Kemal Okem at Prime Minister Benjamin Netanyahu's behest, the Israeli sources said.
Israel had said in a statement on Monday night, in a reference to Erdogan, that those who "systematically violate human rights in their own country should not preach morality to the only true democracy in the region."
It also rejected "baseless smears" from the Turkish leader.
Erdogan has vowed to prevent a draft bill being advanced in Israel that would prevent the use of speakers mounted on minarets to summon Muslims to prayer and accused Israel of apartheid practices.
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Erdogan, a fervent supporter of Palestinians, normalised relations with Israel in June last year after bilateral ties deteriorated over a 2010 Israeli raid on a Gaza-bound ship that killed 10 Turkish activists.
Israeli parliament speaker Yuli Edelstein lashed out at Erdogan on Tuesday, telling public radio that "one mustn't forget: Erdogan was an enemy and will remain one."
"As long as Erdogan leads Turkey the ties (with Israel) won't return to what they were," Edelstein wrote on his Twitter account.
"We must keep correct relations with them," Galant told army radio.
"The fact that from time to time (Erdogan) makes inflammatory remarks that reflect his own rhetorical political interests -- let him talk, we know how to talk too."
"When it comes to practice, I think the Turks have other interests," Galant said, pointing to the number of Israeli tourists who visit Turkey and the possibility of building a pipeline to Turkey to export natural gas from Israel.