Tillerson's trip from Kuwait to the western Saudi city of Jiddah followed discussions on Tuesday with Qatari emir Sheikh Tamim bin Hamad Al Thani that ended with the signing of a counterterrorism pact.
Prior to his visit, Tillerson has maintained contacts with all countries involved in the dispute and other regional actors and has asked, without success, Saudi Arabia and its allies to soften the blockade by warning that it hampers operations against the Islamic State.
He had earlier signed a U.S. -Qatari accord on terrorism financing in an effort to help ease the crisis, but Qatar's opponents said it fell short of allaying their concerns.
Jeddah, Dammam- The states confronting terrorism renewed on Wednesday their insistence on the demands as a condition to restore ties with Qatar, in the conclusion of the quintet meeting in Jeddah that included foreign ministers of Saudi Arabia, UAE, Bahrain and Egypt in addition to the USA secretary of state.
On June 23, Saudi Arabia and its allies released a 13-point list of demands, including the severance of all Qatar's ties with the Muslim Brotherhood and Lebanese Hezbollah resistance movement.
Saudi Crown Prince Mohammed Bin Salman, 31, was appointed to his post last month, less than three weeks after crisis began. Both the United Kingdom and US consider Saudi Arabia a key ally in the fight against extremist groups in the region, and in curbing the influence of Iran, which also accuses Saudi Arabia and its allies of destabilizing the region.
"Reaching a settlement to the crisis is dependent on a positive response from Qatar to these demands, and on the country ending its support for terrorism and terrorist groups", Shoukry was quoted in the statement as saying during Wednesday's meeting.
Kuwait now mediates the crisis.
Qatar has denied the accusations and called the collective decision "unjustified".
Later on Tuesday, the Saudi-led bloc issued a joint statement saying that while it appreciated United States efforts to combat terrorism, more needed to be done.
The four countries said in a joint statement that the deal was the result of their "repeated pressures and demands", adding that it was "not enough".
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