Israeli Prime Minister Benjamin Netanyahu, who is also foreign minister, wrote on Facebook that he had instructed the ministry to hold a "clarification discussion" with Mac Donncha.
Update 9.55pm: What has been described as a "frosty" meeting has taken place between the Irish ambassador to Israel and government officials there.
The Israeli Ministry of Foreign Affairs (MFA) said its deputy director-general for Europe, Rodica Radian-Gordon, expressed "her astonishment and deep disappointment" that the Lord Mayor chose to participate in "such a blatant anti-Israel event".
Interior Minister Arieh Deri ordered an inquiry Wednesday after Mac Donncha announced he was in the West Bank city of Ramallah for a conference after landing at Israel's Ben-Gurion airport.
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Cllr Mac Donncha was able enter Israel and carry on with his planned visit to the West Bank after officials at the Tel Aviv airport let him slip by after they were given a misspelling of his name.
The Israeli government said it expects "an official public response" from the Irish Government with regard to "the conduct of the both the Dublin City Council and of the Lord Mayor".
Councillor Mac Donncha is a supporter of the boycott movement targeting Israel.
Haaretz reported that he has ties with the Ireland Palestine Solidarity Campaign, which promotes a boycott of Israeli businesses and foreign firms who trade in the Jewish state.