The US’s top diplomat was expected to travel back to Qatar today for more talks with the country’s 37-year-old emir, a day after wrapping up discussions with the king of Saudi Arabia and other officials from Arab countries lined up against Qatar.

US Secretary of State Rex Tillerson’s travels have so far not led to any signs of a breakthrough in an increasingly entrenched dispute that has divided some of America’s most important Mideast allies.

Mr. 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.

Saudi Arabia, the United Arab Emirates, Egypt and Bahrain severed relations with Qatar and cut air, sea and land routes with it over a month ago, accusing Doha of supporting extremist groups. Qatar denies the allegations.

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The quartet has given no indication it would be willing to back off from its hard-nosed stance. Just hours before Mr. Tillerson’s arrival in Jiddah, the four Arab states said the counterterrorism deal that Qatar signed with him on Tuesday was “not enough” to ease their concerns.

Mr. Tillerson’s visit to Saudi Arabia included talks with King Salman and his powerful son Mohammed bin Salman, who was recently elevated to the role of crown prince, placing him next in line to the throne. He also met with the foreign ministers of the four countries in the anti-Qatar bloc.

Officials gave little indication of what was discussed, but Mr. Tillerson was likely to press the bloc to ease up on some of its demands after he secured the deal for Qatar to intensify its fight against terrorism and address shortfalls in policing terrorism funding.

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The four anti-Qatar countries last month issued a tough 13-point list of demands that included shutting down Qatar’s flagship al-Jazeera network and other news outlets, cutting ties with Islamist groups such as the Muslim Brotherhood, limiting Qatar’s ties with Iran and expelling Turkish troops stationed in the tiny Gulf country.

Qatar has rejected the demands, saying that agreeing to them wholesale would undermine its sovereignty.

The head of Qatar’s government communication office, Sheikh Saif bin Ahmed al Thani, has accused the quartet of organizing “a smear campaign in the international media to damage Qatar’s reputation” and said they are “not interested in engaging in honest negotiations to resolve our differences.”

The anti-Qatar bloc took partial credit for the US counter-terrorism deal Qatar signed Tuesday, saying it was the result of “repeated pressures and demands” by the four countries and others, but that it failed to go far enough.

While welcoming US-led efforts to dry up terrorist funding, the four maintained a hard line that Qatar must meet their list of what they said were “fair and legitimate demands.”