The four Arab states leading a boycott against Qatar have described Doha’s rejection of their demands as a threat to regional security.
In a statement, Saudi Arabia, Bahrain, Egypt and the United Arab Emirates also warned of unspecified new measures.
Last month the four cut all ties with Qatar, in effect imposing a land blockade on the tiny emirate.
They demanded that Qatar shut down Al Jazeera TV, reduce ties with Iran and end its alleged support for jihadists.
Earlier this week Qatar rejected the Saudi-led bloc’s ultimatum. It denies the allegations against it.
US Secretary of State Rex Tillerson is expected on Monday to visit Kuwait, which is mediating the Gulf crisis.
In Thursday’s statement, Saudi Arabia, Bahrain, Egypt and the UAE said Qatar’s rejection of their 13 demands “reflects its intention to continue its policy, aimed at destabilising security in the region”.
They also threatened new political and economic measures against the Gulf emirate, without providing any further details.
Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani has described the cutting of ties with his country as “a siege that is a clear aggression and an insult”.
“The answer to our disagreement is not blockades and ultimatums, it is dialogue and reason,” he said earlier this week.
The small oil- and gas-rich nation is dependent on imports to meet the basic needs of its population of 2.7 million.
As its only land border is now closed, food is having to be shipped or flown in.
Mr Thani said this could be sustained “indefinitely”.
How did we get here?
- 5 June: A number of Arab countries including Saudi Arabia and Egypt cut diplomatic ties with Qatar, accusing it of destabilising the region. Measures include closing airspace to Qatar Airways
- 8 June: Qatar vows it will “not surrender” the independence of its foreign policy amid US calls for Gulf unity
- 23 June: Qatar is given 10 days to comply with a 13-point list of demands, including shutting down the Doha-based Al Jazeera news network, closing a Turkish military base, cutting ties with the Muslim Brotherhood, and curbing diplomatic relations with Iran
- 1 July: Qatar’s foreign minister says the state has rejected the demands, but is ready to engage in dialogue under the right conditions
- 3 July: Saudi Arabia and its allies extend by 48 hours the deadline for Qatar to accept their list of demands
- 5 July: Qatar again rejects the bloc’s demands.