The expression of support came after Saudi Arabia, the United Arab Emirates, Egypt and Bahrain cut ties with Qatar on June 5, accusing it of support for Islamist militants, an allegation Qatar denies.
Turkey's president said his country "admires and embraces" Qatar's attitude, while slamming the demands by arguing they contradict global law.
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.
QNA said that the rights body had "noted that these violations were shown in several ways, such as not allowing Qatari students to complete exams at the end of the academic year, and refused to give them certificates of graduation and the closure of their educational accounts as well as the termination of their registration arbitrarily without giving reasons".
There were reports earlier this week that Egypt is working with the UAE and Saudi Arabia to slap sanctions on Turkey because of its pro-Qatar stance.
"The siege cannot be subject to restrictions or conditions because it is in contravention of worldwide agreements and human rights conventions", it said. "This list of demands confirms what Qatar has said from the beginning - the illegal blockade has nothing to do with combating terrorism, it is about limiting Qatar's sovereignty", said Sheikh Saif bin Ahmed Al Thani, a Qatari spokesman, in a statement Friday.
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Two tourists walking in New Orleans' French Quarter were attacked and mugged Saturday evening and it was all caught on camera. Surveillance footage shows suspects in the attack on two tourists in New Orleans' French Quarter on Saturday, June 24, 2017.
The request comes two days after the boycotting countries delivered a list of 13 demands to Doha and told the government it has 10 days to comply in order to restore ties with its neighbors.
Bahrain, Yemen and the Maldives have also said they are indefinitely severing ties with Qatar. Kuwait handed the list of collective demands to Doha on Thursday, according to Qatar News Agency.
Under U.S. law, major foreign U.S. arms sales are submitted for review to a small group of lawmakers, including the chairman of the Foreign Relations Committee, before they can go ahead.
Tillerson said in a statement Sunday that several of the demands Saudi Arabia and the other countries have placed on Qatar "will be very hard to meet".
The United States said the demands on Qatar by its Mideast neighbors "will be very hard to meet". Among the key points of the ultimatum is the demand to cut ties with Iran.