Ayub Kara, deputy minister of regional cooperation, said during a visit to the Vatican on Wednesday he was sure the quake that hit central Italy the same day happened because of the resolution, which Israel has said denies the Jewish connection to the city.
"We repudiate the remarks of Deputy Minister Kara," a foreign ministry spokesman said in a statement.
"Since making the statement, Deputy Minister Kara has issued an apology, which is also endorsed by the Ministry of Foreign Affairs," it said.
The condemnation of his remarks came just hours before the start of an official visit to Israel by Italian President Sergio Mattarella.
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The Arab-sponsored resolution passed by the UN cultural agency on October 18 criticised the Jewish state for restricting access to the Al-Aqsa mosque compound in annexed east Jerusalem.
Israel is furious that the UNESCO resolution refers to the holy site in Jerusalem's Old City only by its Muslim name, Al-Aqsa or Al-Haram al-Sharif.
Jews refer to the site as the Temple Mount and it is considered the holiest site in Judaism.
Italy's Prime Minister Matteo Renzi last week described the resolution as "incomprehensible and unacceptable", and said his officials should have voted against it instead of abstaining.
Israel occupied and later annexed Palestinian east Jerusalem in 1967 in a move never recognised by the international community.
UNESCO is responsible for protecting important heritage sites and is one of the few international organisations that recognise Palestine as a member state.