Tensions in the Gulf region have seen countries such as Saudi Arabia boycott Qatari entities - and their measures could impact football fans who wish to wear Neymar and Lionel Messi replica shirts.
"Leaders pointed to Qatar - look!", he said.
On June 5, Bahrain, Saudi Arabia, Egypt, the United Arab Emirates, as well as Yemen, the interim government of Libya, Mauritius and the Maldives announced they severed diplomatic relations with Qatar, accusing Doha of supporting terrorism and extremist ideology, of hostile policy and meddling in the affairs of the Arab states.
For years, Gulf states and Egypt have resented Qatar's ties to the moderate Muslim Brotherhood movement along with its sponsorship of the pan-Arab television network al-Jazeera.
US President Donald Trump has accused Qatar's leadership of bankrolling extremists and demanded a halt to that funding, drawing praise from Saudi Arabia and its allies.
The rights group says that, according to Qatar's National Human Rights Committee, more than 11,000 nationals of Bahrain, Saudi Arabia and UAE live in Qatar.
On Saturday, Saudi Arabia, Bahrain and the UAE made no mention of Mr Tillerson's call.
Saudi Arabia said it was committed to "decisive and swift action to cut off all funding sources for terrorism" in a statement carried by the state news agency SPA, while Bahrain hailed US efforts to ensure "international solidarity" on the issue.
Student stuck on NY subway gets improvised graduation
The graduating senior, dressed in full cap and gown, knew after 45 minutes that he would be late to the ceremony. Alcantara said this commute to school took longer than any other train ride he has take in the last four years.
The incident triggered a diplomatic row between Qatar and its neighbors.
The State Department had said the USA learned only at the last minute about the Arab nations' plan to cut ties. "Process can only work following clear indication that Qatar will stop support & finance of extremism & terrorism".
Dialogue is the best way to tackle the political rift in the Arab world over Qatar, two top diplomats said Saturday in Moscow.
Russian Foreign Minister Sergey Lavrov met with his Qatari counterpart, Sheikh Mohammed bin Abdulrahman Al-Thani, in the Russian capital.
"For us, unity is clearly necessary for maximum effect on this front (against terrorism)", he said.
Mr Erdogan was meeting Bahrain's foreign minister on Saturday. "We can not be happy in a situation when the relations between our partners are worsening".
A separate SPA report on Saturday acknowledged Tillerson's call for Qatar to curtail support for terrorism, without mentioning that he had also said the crisis was hurting ordinary Qataris, impairing business and harming the USA fight against the Islamic State militant group.
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