The President extended similar condolences to the government and people of Iraq over the human and material losses suffered in the wake of the quake on their border with Iran.
Prime Minister Benjamin Netanyahu told the leaders of the Jewish Federations of North America's annual meeting this week that he offered assistance to the victims of the devastating quake that killed hundreds in both countries.
Netanyahu said the offer was made through the International Committee of the Red Cross and Israeli media reported that Iran promptly turned it down.
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"I just saw the pictures of the destruction in Iran and Iraq from this week's natural disaster".
Pakistani president and the prime minister had sent messages of solidarity with the Iranian people and offered all possible support by Pakistan in this hour of need. Israel continues to be a light unto the nations and this is what I am proud of.
President Buhari's message comes three days after Vice President Yemi Osinbajo condoled with the government and people of Iran on the disaster caused by the quake.
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A spokesperson from Netanyahu's office said later on Tuesday that the assistance had been "immediately rejected".
Israel has still railed against the deal, arguing that it hands the Iranian regime hundreds of millions of dollars back in frozen assets it can use to fund proxy groups in the Middle East. Kermanshah, the western province, is most affected by the disaster.
Senator Bernie Sanders and four Democratic senators demanded that the State Department partially wave sanctions on Iran to assist the estimated 70,00 people who lost their homes following the 7.3-magnitude quake on Sunday.
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Neither Iran and Iraq recognize Israel's right to exist.