Speaking outside a mosque in Istanbul, the Islamist president said putting the 13 demands to Qatar "is against global law because you can not attack or intervene in the sovereignty of a country". Tillerson called on all parties to lower their rhetoric and to seek unity in the fight against terrorism.
"Tehran stands alongside the people and government of Qatar and we believe that... pressure, threats and sanctions are not a good solution to solve problems" between countries of the region, Rouhani added.
"Even though they still didn't come back to us on this, asking Turkey to pull back its troops [from Qatar] is disrespectful against Turkey", he said. That Qatar hosts a large United States military base and has the backing of North Atlantic Treaty Organisation member Turkey likely makes any sort of attempt to oust the Emir by force virtually impossible.
The four countries also want Qatar to reduce its ties with Iran and close a Turkish military base, setting a deadline on Friday of 10 days.
In wake of the economic and diplomatic blockade, Iran began delivering over 1,100 tons of food products to Qatar daily through its Dayyer and Bolkheir Ports in the Persian Gulf.
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U.S. Secretary of State Rex Tillerson seems to be siding with Qatar in some of the demands made by the Gulf States in exchange for the removal of blockades.
The crisis erupted on June 5 when Saudi Arabia, the United Arab Emirates, Bahrain, Egypt, and others broke ties with Qatar, accusing it of backing extremism, a claim Doha denies. "It is about limiting Qatar's sovereignty, and outsourcing our foreign policy", Sheikh Saif al-Thani, director of Qatar's government communications office, said.
Doha, whose neighbours have closed their airspace to Qatari flights, has said it was reviewing the list of 13 demands, but said it was not reasonable or actionable.
At the end of his remarks, he said the Islamic world required unity and integrity and the two countries could undoubtedly work together in these arenas. "It is a breach of Qatar's sovereign rights".
Qatar has said it will not comply with the demands ahead of the 3 July deadline, and it is not clear what the Saudi response will be when it passes.
That claim contradicts the UAE's ambassador to Washington, Yousef al-Otaiba, who told Fox News the charges of Qatar supporting extremists had been raised in a meeting three years ago chaired by the late Saudi King Abdullah.