The US also has a large military base in Qatar and the Pentagon has voiced support for Qatar's fight against Islamic State (IS) militants in Syria and Iraq.
The four-nation bloc has to tread a fine line between pressuring Qatar without alienating an worldwide community with no appetite for further conflict in the region, said Graham Griffiths, an analyst at global risk consultancy Control Risks in Dubai.
Qatar has denied any support for extremism and accused the countries of seeking to infringe on its sovereignty.
Foreign ministers of the Saudi-led bloc that imposed an embargo on Qatar said Wednesday they regretted the emirate's "negative" response to a list of demands to end a diplomatic crisis. That deadline expired early Wednesday morning.
The statement was issued after the foreign ministers of Saudi Arabia, the UAE, Egypt and Bahrain held a meeting in Cairo.
The Turkish base was built in Qatar after getting the go ahead but now Saudi Arabia wants it to be closed as part of demands directed to Doha in the ongoing crisis in the Arab Gulf.
Saad Sherida al-Kaabi, the company's CEO, told reporters on Tuesday that Qatar Petroleum intends to raise production from 77 million tonnes of natural gas to 100 million tonnes a year by 2024.
Gulf officials have said the demands are not negotiable, signalling more sanctions are possible, including "parting ways" with Doha - a suggestion it may be ejected from the GCC, a regional economic and security cooperation body founded in 1981.
"You have to ask what the next step is" for Qatar's leader, said Kattouf, former USA ambassador to Syria and the United Arab Emirates .
"There is no deviation from the important and effective measures that had to be applied in cases where there is sponsorships of states and individuals of terrorist organizations and activities", Egypt's Foreign Minister, Sameh Shoukry said. He said Germany supported the UAE's efforts at confronting those who fund extremists.
"The matter from the beginning was not up for negotiations. there is no middle ground", he said.
"We, as Al-Jazeera employees, will continue to work with professionalism, until the very last moment".
If Qatar is eventually expelled from the GCC, it will disrupt the geopolitical balance of the region more than doing any big harm to Doha.
Qatari foreign minister Sheikh Mohammed bin Abdulrahman al-Thani told a session of London's Chatham House think tank that Doha was continuing to call for dialogue to settle the dispute.
"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", Sheikh Abdullah said.
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