The foreign ministers of Bahrain, Saudi Arabia, Egypt and the United Arab Emirates (UAE) met in the Bahraini capital Manama to discuss the crisis that has raised tensions across the region.
Diplomatic efforts led by Kuwait and backed by Western powers have failed to end the dispute, in which the four states have severed travel and communications with Qatar.
"The four countries are ready for dialogue with Qatar with the condition that it announces its sincere willingness to stop funding terrorism and extremism and its commitment to not interfere in other countries' foreign affairs and respond to the 13 demands," Bahrain's foreign minister, Sheikh Khalid bin Ahmed al-Khalifa, told a joint news conference after the meeting.
They announced no new economic sanctions on the Gulf state.
Saudi Arabia, UAE, Egypt and Bahrain have previously issued a list of 13 demands for Qatar, which include curtailing its support for the Muslim Brotherhood, shutting down the Doha-based Al Jazeera channel, closing a Turkish military base and downgrading its relations with Gulf enemy Iran.
Saudi Foreign Minister Adel al-Jubeir said Qatar was not serious in tackling the countries' demands.
Saudi Foreign Minister Adel al-Jubeir (R) and Bahraini Foreign Minister Khalid bin Ahmed al-Khalifa have six principles for Qatar to adopt. Source: EPA, AAP
"We are ready to talk with Qatar on the implementation of the demands, on the implementation of the principles, if Qatar is serious, but it has been clear that it is not," he said.
The four countries have also listed "six principles" they want Qatar to adopt.
The Saudi-led bloc cut ties with the Gulf state on June 5, accusing it of backing militant groups and cosying up to their arch-foe Iran, allegations Doha denies.
Earlier on Sunday, al-Hayat newspaper said, citing unidentified Gulf sources, that the four countries "are expectedto impose sanctions that will gradually affect the Qatari economy."
Saudi Arabia has closed its land border with Qatar while all four countries have cut air and sea links with Doha, demanding the gas exporting country take several measures to show it was changing its policies.
Turkey and Iran have stepped in to provide fresh produce, poultry and dairy products to Qatar instead of Saudi Arabia and the UAE, with Oman providing alternative ports to those in the UAE.
The four Arab countries added 18 more groups and individuals they say are linked to Qatar to their "terrorist" lists last week.
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