In their statement, which was released early Friday, the four countries said Qatar's refusal to abide by their proposals "reflects the extent to which they are linked to terrorism and its continued attempt to sabotage, undermine security and stability" in the region, the state-run Saudi Press Agency reported.
They accused the Persian Gulf country of "deliberately" undermining the regional security and harming "the interests of the peoples of the region."
They also thanked Kuwaiti Emir Sabah al-Ahmad al-Jaber al-Sabah for acting as mediator and blasted Qatar for "disregarding" him in an attempt to "return the crisis to the starting point."
The four allies severed ties with Qatar on June 5, officially accusing Doha of supporting "terrorism" and destabilizing the Middle East, allegations that Qatar says are unjustified and stem from false claims and assumptions.
In their apparent bid to win more support from the US and Israel, the Arab countries have suspended all land, air and sea traffic with Qatar, expelled its diplomats and ordered Qatari citizens to leave their countries.
Saudi Arabia completely shuttered the land border with Qatar in order to cripple the neighboring country's food supply. In response, Qatari leaders turned to Iran and Turkey to keep the chain running.
Shutting down the Doha-based Al Jazeera broadcaster, severing diplomatic ties with Iran, closing down a Turkish military base in Qatar and paying an unspecified sum in reparations were some of the demands that Qatar had received.
Doha says the siege is a "clear aggression" and the demands put forward to remove it are "unrealistic."
Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani said Wednesday Riyadh and its allies were asking Qatar to "surrender... [its] sovereignty to end the siege."
He also ruled out chances of a rapid reconciliation and said his country was preparing for a wider diplomatic rift.