The Lord Mayor of Dublin Micheál Mac Donncha narrowly avoided detention and expulsion by Israeli authorities when he landed at Ben Gurion Airport in the country.
MacDonncha, however, was already in Ramallah, in the occupied West Bank, having flow in through Tel Aviv airport.
The Israeli government says the Lord Mayor is attending a conference in Ramallah in Palestine that they describe as "anti-Israel".
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.
Donncha managed to enter Ramallah via Israel on Tuesday despite a ban imposed on him by the state.
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"This is especially disturbing when taken in context with the timing of the event - the week during which Israel marks the Holocaust", the MFA said.
Israel expects a "public and formal" response from the Republic to his conduct, it said.
Earlier in the week, the Dublin City Council urged the Irish government to boycott Israel and expel its ambassador from Ireland over the killings of protesters in Palestine.
Israel ordered a probe Wednesday into how Mac Donncha was allowed into the country.
Israel's interior ministry and strategic affairs ministry blamed each other for the mix-up, it said.