The demands included: Cutting back Qatar's diplomatic ties to Iran, shuttering the Qatari media outlet "Al-Jazeera", ending the military presence of Turkey in Qatar and ending any military cooperation with it.
"There is no fear".
Qatari officials say the demands are so strict that the four countries never seriously intended them as a negotiating position and see them as being aimed at hobbling Doha's sovereignty.
"He reiterated the importance of stopping terrorist financing and discrediting extremist ideology", the White House said.
Foreign ministers of nations boycotting Qatar will meet in Cairo on Wednesday to discuss their next steps.
Qatar is at the center of the biggest diplomatic crisis in the Middle East in decades, which started in early June when nine allies, led by Saudi Arabia, froze ties with the country over its alleged support of terrorism.
The ultimatum expires Monday, though the countries involved have not provided a precise time or detailed what immediate penalties, if any, Qatar will face.
The summit brings together leaders including U.S. President Donald Trump, Turkish President Recep Erdogan and Russian President Vladimir Putin.
The countries who had imposed sanctions against Qatar had sent an ultimatum having 13 points and a 10-day deadline, which was supposed to end today.
A group of Arab nations have extended a deadline for Qatar to respond to their list of demands in a diplomatic crisis roiling the Gulf, saying Kuwait's emir requested the delay as part of his efforts to mediate the dispute.
A defiant Qatar has claimed the demands were deliberately "made to be rejected".
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