Greece said it is "profoundly saddened by the passing of United Arab Emirates President Sheikh Khalifa bin Zayed Al Nahyan" on Twitter on Friday.
"During his tenure, Greece-UAE relations have expanded exponentially. We extend our sincere condolences and deepest sympathy to his family, the people and government of our close friend and strategic partner the United Arab Emirates," it added.
Sheikh Khalifa bin Zayed Al Nahyan, who was 73, became the leader of the richest emirate, Abu Dhabi, in 2004.
He was president of the UAE since 2004, but his role had been largely ceremonial since he suffered a stroke in 2014, BBC reported.
His half-brother, Mohamed bin Zayed al-Nahyan, is now in charge of state affairs.
The al-Nahyan family is believed to have a fortune of $150bn (£123bn).
As well as being president of the UAE, Sheikh Khalifa was also the ruler of Abu Dhabi, the oil-rich capital of the seven emirates which comprise the UAE.
News of his death was announced by the official WAM news agency.
The ministry of presidential affairs declared 40 days of mourning with flags at half-mast from Friday, and work suspended in the public and private sector for the first three days.
Sheikh Khalifa took over as the UAE's second president in November 2004, succeeding his father as the 16th ruler of Abu Dhabi.
In the first decade of his rule, he presided over a major restructuring of both the federal government and that of Abu Dhabi.
But after his stroke, he was rarely seen in public, although he continued to issue rulings.
Elsewhere, Greece and Bahrain support positions of principle that are always based on international legality, Foreign Minister Nikos Dendias said in joint statements with visiting Foreign Minister of Bahrain, Abdullatif bin Rashid Al Zayani, following their meeting in Athens on Friday.
Dendias warmly thanked his counterpart for "Bahrain's support within the context of UNESCO, as well as Bahrain's position regarding the conversion of Hagia Sophia, a monument of international cultural heritage, into a mosque."
"Our common principles and values are clear, they are respect for international law and respect for the United Nations Convention on the Law of the Sea (UNCLOS), which both countries have ratified and implement without fail," Dendias underlined.
He noted that both Greece and Bahrain are candidates for the UN Security Council, Greece for 2024-2025 and Bahrain for 2025-2026. Dendias also pointed out that this was their third meeting in a few months, as Dendias had recently visited Manama, while the foreign minister of Bahrain participated in the Friendship Forum held in Athens in February 2022.
The Greek minister said that he was looking forward to deepening the already excellent bilateral relations of the two countries, while a series of agreements will be signed during Prime Minister Kyriakos Mitsotakis' visit to Manama.
"Greece wishes to deepen its collaboration with the Gulf Cooperation Council," he said, adding that Greece will continue its efforts to strengthen ties with all the countries in the Gulf.
Finally, he expressed a desire to visit the region, particularly Bahrain.
On his part, Al Zayani referred to the historic ties and constructive collaboration between Greece and Bahrain, noting that relations were going through a period of development and growth in many sectors and at all levels.
"We pointed out the need to enhance our bilateral relations in the economic, trade, investment, cultural, tourism, technological and environmental sectors," he noted, as well as "the need to make use of a climate that attracts investments to both countries, exploring sectors of commercial collaboration and the strengthening of joint ventures."
Developments in Ukraine and their consequences for stability and security in Europe were also discussed, as well as the need to arrive at a peaceful, permanent and stable settlement through negotiations and diplomacy, in a UN framework.