The four Arab states leading a boycott against Qatar have described Doha’s rejection of their demands as a threat to regional security.
Last month the four cut all ties with Qatar, in effect imposing a land blockade on the tiny emirate.
Earlier this week Qatar rejected the Saudi-led bloc’s ultimatum. It denies the allegations against it.
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”.