"Meeting on the sidelines of a regional security summit in Kazakhstan, Chinese Foreign Minister Wang Yi told Iranian Foreign Minister Mohammad Javad Zarif that peace and stability in the Gulf accords with the common interests of the region and the global community".
Questions have also been raised over whether Qatar should retain the right to host the 2022 football World Cup and over its economic ability to sustain the crisis.
Some African countries have cautiously come out in support of attempts to isolate Qatar.
"For Qatar, we want you back among the unity of responsible nations", Trump said, calling on the Gulf nation to stop funding terrorism and teaching hate.
Kuwait - which unlike most of its fellow Gulf Cooperation Council members has not cut off ties with Qatar - has been leading efforts to mediate.
"These drastic measures are already having a brutal effect, splitting children from parents and husbands from wives", said Amnesty after its researchers interviewed dozens of people affected by the crisis.
But Sheikh Mohammed told the AP on Thursday that Sheikh Tamim "is not going to leave the country while the country is in blockade", in effect turning down the mediation offer. Iran also has sent four cargo planes of food to Qatar and plans to provide 100 tons of fruit and vegetable every day, Iranian officials said.More news: Gulf states announce humanitarian hotline for mixed Qatari families
On Friday Saudi Arabia, Bahrain, the UAE and Egypt tightened their squeeze on Qatar by putting dozens of figures and charities they link to the country on terrorism blacklists.
Arab countries have put 12 organizations and 59 people they say are associated with energy rich Qatar on a terror sanctions list.
The three Gulf nations said early Sunday that officials would consider "humanitarian cases" as a deadline looms for Qataris to return home.
Qatar protested the unjustified decision of Bahrain, Saudi Arabia, Egypt and the United Arab Emirates to cut ties with the country.
For its part, Qatar issued an overnight statement saying residents living in the country from nations that severed ties would have "complete freedom" to stay despite the "hostile and tendentious campaigns" now targeting it.