The original 10-day deadline for Qatar to comply with the demands expired on Sunday but was extended to Wednesday at the request of Kuwait, which is acting as mediator.
The four countries accuse Doha of harbouring Islamist groups that they consider terrorist organisations - including the Muslim Brotherhood - and giving them a platform on the Al Jazeera satellite channel, which is funded by the Qatari state.
Stressing that Doha had consistently called for resolving the crisis through dialogue, he said Qatar had always supported the global fight against terrorism - despite assertions to the contrary now emanating from Riyadh, Abu Dhabi and Cairo.
State-owned Qatar Petroleum said it would go ahead with the output boost regardless of whether or not Saudi Arabia and its allies maintain a sweeping embargo they imposed last month.
Qatar Airways said on Thursday that passengers travelling to the U.S. can now carry their laptops and other large electronics on board, ending a three-month in-cabin ban on devices for the Doha-based airline.
Saudi Foreign Minister Adel al-Jubeir, at a joint press conference, said that further steps against Qatar will be taken at the appropriate time in line with the worldwide law. The timing of the latest announcement is likely to be seen as as much political as economic as Qatar is locked in the Gulf's worst diplomatic crisis in years.
Moody's has said it expects "the stalemate may continue for some time", and added: "Depending on the duration and potential further escalation of tensions, the dispute could negatively affect Qatar's economic and fiscal strength".
"Clearly the blockading countries did not submit their demands with the expectation that they would provide a framework for resolving their differences with Qatar", he said in his address to the think tank.
Trying to find reasons behind Qatar's royal family's support to terrorism, an article published in the New Republic explained that it is just a continuation of a bad decision made by former Qatari ruler and the incumbent emir's father, Sheikh Hamad bin Khalifa Al Thani, and his foreign minister and prime minister, Sheikh Hamad bin Jassim bin Jaber al Thani.
Ahead of the Cairo meeting, Donald Trump called Egyptian President Abdel Fattah El Sisi over the Gulf crisis.
Without resolution, even more punitive actions are possible that would compound Qatar's woes: Bahrain's foreign minister would not rule out expelling Qatar from the Gulf Cooperation Council.
"We remain loyal to our agreement with Qatar".
It warned that this carried the risk that Qatar's sovereign credit fundamentals could be negatively affected.
While the rejection of the ultimatum was met angrily on Wednesday by the Saudis and other countries, which vowed to continue the blockade until their demands were met, Gabriel claimed that the situation around Qatar had actually improved, as the blockading countries did not reiterate once again many of their demands.