The minister, Adel al-Jubeir, told journalists in London that Qatar should respond to demands to halt its support for "extremism and terrorism" which, he said, were being made by the whole world and not just Gulf states.
Four Arab states - Saudi Arabia, the UAE, Bahrain and Egypt - severed diplomatic relations with Qatar on June 5, accusing it of supporting Islamist militants and Iran - charges that Doha has denied. The UAE has also decided to blacklist Qatari individuals and entities.
The political crisis in the Gulf prompted U.S. Secretary of State Rex Tillerson to announce on Friday that he was cancelling his planned trip next week to attend an Organization of American States meeting in Mexico to instead remain in Washington to work on reducing diplomatic strains.
Tillerson "will continue his efforts to de-escalate tensions in the Middle East region through in-person meetings and phone conversations with Gulf and regional leaders," the U.S. State Department said in a statement. It also said U.S. Deputy Secretary of State John Sullivan would attend the OAS meeting.
Jubeir said the list being compiled by the four Arab countries were not "demands," but "a list of grievances that need to be addressed and that the Qataris need to fix."
"We are working on those with our Bahraini, Emirati and Egyptian partners in order to compile this list and present it to the Qataris, and I think it will be done fairly soon."
Calling Doha an "ally" in the six-country Gulf Cooperation Council (GCC), Jubeir said there was no intention of harming the Qatari people.
"Enough is enough, and our Qatari brothers cannot continue to fund extremism and terrorize and incite and use hostile media and interfere with the affairs of other countries and still remain in good standing," he said, adding he expected a positive response that would move the region to a "better place."
Jubeir did not detail what demands could be made.
But his comments echoed those of the UAE's ambassador to the United States, who said on Tuesday the list would broadly address three areas of support for terrorism, meddling in the internal affairs of the four Arab states and attacks through Qatari-owned media platforms.