Interior Minister Aryeh Deri had previously ordered border control officers to block Mac Donncha from entering the country, but he entered via Ben Gurion Airport on Wednesday due to an administrative mishap (someone spelled his name wrong at passport control).
Ireland's ambassador to Israel, Alison Kelly, was then called before the Foreign Ministry to explain the Lord Mayor's actions.
MacDonncha, however, was already in Ramallah, in the occupied West Bank, having flow in through Tel Aviv airport.
Sinn Fein councillor Michael Mac Donncha claims he was unaware of his ban when he arrived in Israel on Tuesday night.
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.
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However, the SGPC maintains that the film contains objectionable content regarding the Sikh guru and his family. The apex court pointed out that the CBFC had already cleared the film for release.
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Authorities there say Mícheál Mac Donncha was attending a conference in Palestine that glorified a war criminal.
The paper said he has ties with the Ireland Palestine Solidarity Campaign, which promotes a boycott of Israeli businesses and foreign firms which trade in the Jewish state.
The ministry said in a statement that Israel expresses its "deep disappointment and shock" over the incident.
At least 31 Palestinians have been killed by cross-border gunfire by the Israeli army since March 30 when peaceful rallies began along the Gaza Strip's roughly 45-kilometer eastern border with Israel.