The foreign ministers of Bahrain, Saudi Arabia, Egypt and the United Arab Emirates met in the Bahraini capital, Manama, to discuss the crisis that has raised tensions across the region.
The Saudi-led bloc cut ties with the Gulf state on June 5, accusing it of backing terrorist groups and cosying up to their arch-foe Iran, allegations that Doha denies.
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 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.
"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.
Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani dismissed Sunday's statement from the four countries and said sanctions were violating international laws.
"There isn't a clear vision (from Manama's meeting), there is only a stubborn policy from the blockading countries and refusal to admit that these are illegal actions," Sheikh Mohammed told Al Jazeera TV channel.
Earlier on Sunday, al-Hayat newspaper said, citing unidentified Gulf sources, that the four countries "are expected to 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 groups and individuals they say are linked to Qatar to their "terrorist" lists last week.
(Reporting by Sami Aboudi and Omar Fahmy; Additional reporting by Mostafa Hashem in Doha; Editing by Jane Merriman and Peter Cooney)
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