Details of the response were not immediately available, but a Gulf official told AFP that Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman Al-Thani had delivered it during a short visit to Kuwait, which is acting as a mediator in the crisis.
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt had announced in the early hours of today they were pushing back a deadline for Qatar to agree to a list of 13 demands they issued on June 22.
The demands included Doha ending support for the Muslim Brotherhood, closing broadcaster Al-Jazeera, downgrading diplomatic ties with Iran and shutting down a Turkish military base in the emirate.
Sheikh Mohammed had earlier said the list of demands was "made to be rejected".
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Saudi Arabia and its allies announced on June 5 they were severing ties with their Gulf neighbour, sparking the worst diplomatic crisis to hit the region in decades.
They accused Qatar of supporting extremism and of being too close to Saudi Arabia's regional arch-rival Iran, which Doha has strongly denied.
German Foreign Minister Sigmar Gabriel, who today starts a tour of several Gulf states, called for "serious dialogue" to end the crisis.
"We are worried that the distrust and the disunity could weaken all the parties concerned as well as the entire peninsula," said Gabriel, who will visit Saudi Arabia, the United Arab Emirates and Qatar.
Riyadh and its supporters have already severed air, sea and ground links with Qatar, cutting off vital routes for imports including food.
It is unclear what further measures will be taken if Qatar fails to meet the demands, but the UAE's ambassador to Russia Omar Ghobash warned last week that further sanctions could be imposed.
As well as expelling Qatar from the six-member Gulf Cooperation Council, Riyadh and its allies could tell their economic partners to choose between business with them or with Doha, he told Britain's Guardian newspaper.
Qatar has long pursued a more independent foreign policy than many of its neighbours, who tend to follow the lead of regional powerhouse Saudi Arabia.
US Secretary of State Rex Tillerson has also called for compromise and hosted senior Gulf officials, but his efforts have been undermined by remarks from President Donald Trump apparently supporting Riyadh's position.
Trump spoke separately yesterday with the Saudi king, Abu Dhabi's crown prince and the Qatari emir on his concerns over the dispute, the White House said.
Trump "underscored that unity in the region is critical," the statement said, but also "reiterated the importance of stopping terrorist financing and discrediting extremist ideology."
The 13 demands have not been officially published, but a Kuwaiti diplomatic source confirmed today that the list as it has appeared in the media was genuine.