But Trump said that he, Tillerson and military leaders had decided during Trump's trip to Saudi Arabia last month that a public rebuke was needed.
Saudi Arabia, the United Arab Emirates, Egypt and Bahrain lead a string of countries that this week cut ties with Qatar over what they say is the emirate´s financing of extremist groups and its ties to Iran, Saudi Arabia´s regional arch-rival. Qatar's neighbors have also criticized Qatar for allegedly supporting groups like the Muslim Brotherhood and Hamas. The Qatari Foreign Ministry said in a statement that the two held talks on how to "restore normal relations" in the Gulf.
The move comes as Bahrain criminalized any show of support on social media in a bid to further isolate Qatar, which has been accused of supporting terrorism and destabilizing the region.
In all, 59 people and entities were listed. The list later expanded to nine, with the addition of Mauritius, Mauritania and Libya's eastern-based government.
"Our position on countering terrorism is stronger than numerous signatories of the joint statement - a fact that has been conveniently ignored by the authors".
"We lead the region in attacking the roots of terrorism", the government statement said.
Turkey, meanwhile, has approved a bill allowing more troops to be based in Qatar.
Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani called the moves by Arab neighbours and others "clear violations of global law and worldwide humanitarian law".
Turkey, which works closely with Qatar in the energy sector, has walked a fine line between defending Qatar and abstaining from openly antagonising Saudi Arabia.
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And denouncing the blacklist, Sheikh Mohammed added: "There is a continuous escalation from these countries. but our strategic options are still diplomacy and dialogue".
According to Qatari officials, during the call President Trump "expressed his readiness to find a solution to the diplomatic crisis in the Gulf, stressing his keenness on maintaining stability in the Gulf".
So far, European countries have largely stayed on the sidelines in the dispute.
Sheikh Mohammed is expected in Moscow Saturday to meet Foreign Minister Sergei Lavrov, and officials said Friday he also spoke with Tillerson by telephone. They also gave Qatari citizens 14 days to depart their respective countries and banned their citizens from visiting the country.
Kuwait - which unlike most of its fellow Gulf Cooperation Council (GCC) members has not cut ties with Qatar - has led mediation efforts. A Qatari diplomat told the Associated Press on Thursday that his country's emir, Sheikh Tamim bin Hamad Al Thani, won't travel overseas while the blockade remains in place.
Tillerson told reporters at the State Department shortly before Trump spoke that this blockade is hindering the US -led military campaign against ISIS, creating hardships for the people of Qatar and "impairing USA and other worldwide business activities in the region".
Qatar is the world's largest exporter of Liquefied Natural Gas, but industry experts say shipowners are seeking clarity on the UAE's ban on Qatari-linked vessels calling at its ports.
The call also comes amid reports that Russian hackers were suspected of interfering with a news site in Qatar and may have put out fake information that helped spark the diplomatic crisis in the Gulf, CBS News has learned.
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