In retaliation to Naeh's expulsion, Israel ordered the Turkish consul-general in Jerusalem to return home for consultations.
Turkey's ambassadors to both Tel Aviv and Washington had already been recalled. Turkey summoned Israel's consul-general in Istanbul following Turkoglu's expulsion, and also asked him to leave the country.
An Israeli television channel aired recordings from 2015 earlier this year, in which he pressured an Israeli gas tycoon's son for money for a prostitute, using a controversial gas deal as leverage.
The recordings come as Israeli police continue their investigation into suspicions that the prime minister received gifts from tycoons in exchange for political favours.
South Africa also recalled its ambassador from Tel Aviv.