"While some of the elements will be very hard for Qatar to meet, there are significant areas which provide a basis for ongoing dialogue leading to resolution".
Diplomatic relations were cut with Qatar by four Arab neighbors including Saudi Arabia, the United Arab Emirates, Bahrain and Egypt on June 5 who accused the small oil-rich country of having ties with "terrorist organizations", including the Muslim Brotherhood.
Last week, the four Arab countries reportedly gave Qatar 10 days to comply with a list of 13 demands to end the crisis, insisting, among others, that Qatar close the same Turkish military base that Khalifa had acknowledged as helping in the protection of the region's security during his Turkey visit earlier this month.
Meanwhile, Tillerson on Sunday said in a statement that Qatar is reviewing demands by neighbouring Gulf nations to end the weeks-long diplomatic dispute.
"The disagreement with Qatar is a political and security dispute and has never been military", the Bahraini foreign minister said on Twitter.
Mr Tillerson is also calling for a "lowering of rhetoric" to "help ease the tension" and said the United States is supporting Kuwait's efforts to mediate.
Qatar denies the allegations against it and says the demands are aimed at curbing its sovereignty.More news: Lyon sign 21 year old Chelsea owned Burkina Faso striker
The director of the Qatari's communication office said the blockade was meant to "limit Qatar's sovereignty and interfere in its foreign policy", according to the official QNA news agency.
"Demanding that Turkey pull its soldiers is unfortunately also disrespectful toward Turkey", he said.
"NHRC noted that Qatar's acceptance of these demands and conditions would subject the country to global accountability and violate its obligations on human rights conventions".
"We view cooperation with the Qatari government as continuous cooperation and believe that there are very good opportunities to further deepen relations between the two countries and these opportunities must be exploited", Rouhani said, according to statement on his website.
Erdogan called the demand that Qatar shut down Al-Jazeera an attempt to take away the network's press freedom and urged rights groups to speak out against that.
Qatar's foreign minister is set to meet his U.S. counterpart in Washington, DC, after the USA state department voiced confusion over the Saudi-backed embargo of the country.