Doha's response, they said, was "not serious" and betrayed Qatar's "failure" to realise the gravity of the situation.
The announcement followed a meeting by foreign ministers from the four nations, Saudi Arabia, Egypt, the United Arab Emirates and Bahrain in Cairo, shortly after they said they had received Doha's reply.
The four accuse Qatar of supporting terror groups and also of maintaining close relations with Shiite power Iran - Saudi Arabia's nemesis. They also say Qatar must stop meddling in their affairs.
It did not "lay the foundations for Qatar's abandonment of the policies it pursues. It's a position that does not realize the gravity of the situation," he added.
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The ministers did not say what their next steps would be that, they explained, would be announced after further consultations. They will meet next in Bahrain, but a date has yet to be set.
"We hope wisdom will prevail and Qatar will eventually make the right decisions," Shukri added.
Some of the rhetoric by the four ministers, however, was clearly belligerent.
Shukri said Qatar's policies could not be allowed to continue and vowed that Egyptian blood would not be shed in vain, a reference to deadly attacks by militants on Egyptian army and security forces. Cairo has long accused Qatar of supporting extremists in Egypt.
Earlier today, US President Donald Trump, called on all parties in the dispute to "negotiate constructively" and to "stop terrorist financing and discredit extremist ideology."
A White House statement said Trump's call for a negotiated settlement came in a telephone conversation with Egyptian President Abdel-Fattah el-Sissi.
The four nations issued a 13-point list of demands on June 22, giving Qatar 10 days to comply. They later extended the deadline by another 48 hours at the request of Kuwait, which is trying to mediate the crisis. That second deadline expired early Wednesday morning.
Yesterday, intelligence chiefs from the four Arab countries met in Cairo, likely to discuss the crisis, according to Egypt's state MENA news agency.
The crisis has become a global concern as neither side appears to be backing down. Qatar, the world's biggest exporter of liquefied natural gas, hosts some 10,000 American troops at its sprawling al-Udeid Air Base. US Secretary of State Rex Tillerson has been trying to ease tensions, while Trump's earlier comments on Qatar funding extremist groups back the four countries' position.
German Foreign Minister Sigmar Gabriel yesterday visited officials in both the United Arab Emirates and Qatar. He said Germany supported the UAE's efforts at confronting those who fund extremists but also urged the GCC to find common ground. "For us (Europeans), the GCC is the guarantor of stability and security in the region," he said.
"To defeat terrorism, we must confront extremism, we must confront hate speech, we must confront the harboring and sheltering of extremists and terrorists, and funding them," he said. "Unfortunately, we in this region see that our sister nation of Qatar has allowed and harbored and encouraged all of this."
Qatar's foreign minister, Sheikh Mohammed bin Abdulrahman Al Thani, criticized the four Arab nations for trying to isolate Qatar "under the banner of fighting terrorism."
Though Qatar Airways' routes over its neighbors have been closed, along with the country's sole land border with Saudi Arabia, Doha has been able to import food and goods from other countries. Its economy, fueled by its natural gas exports, seems to be weathering the crisis though there has been pressure on its stock market and currency.
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