DUBAI, United Arab Emirates — Four Arab countries isolating Qatar vowed today to take additional steps against the energy rich Gulf state after it refused to accept their demands over allegations that it supports extremist ideology.

Saudi Arabia, the United Arab Emirates, Egypt and Bahrain accused Qatar in a joint statement carried on Gulf state media of thwarting all efforts aimed at resolving the rift and said it intends to “continue its policy aimed at destabilizing security of the region.”

They vowed to “take all necessary political, economic and legal measures” against Qatar in a “timely manner.” They did not specify what those steps could include, though officials have previously suggested they could intensify efforts to isolate Qatar economically.

The four countries cut diplomatic ties and severed air, land and sea links with World Cup 2022 host Qatar early last month. They later issued a 10-day ultimatum to a 13-point list of demands that included cutting ties with terrorist groups, curbing relations with Iran and shutting media outlets including Al-Jazeera.

Qatar has strenuously denied that it supports extremist groups. It is refusing to shutter Al-Jazeera, one of its best-known brands, and sees the ultimatum as an affront to its sovereignty.