Although further sanctions have been threatened if Doha does not capitulate, the UAE's foreign minister Anwar Gargash has played down the chances of an escalation, saying "the alternative is not escalation but parting ways", suggesting Qatar may be forced out of the Gulf Cooperative Council (GCC).
German Foreign Minister Sigmar Gabriel, who on Monday starts a tour of several Arab states, called for a "serious dialogue" to end the crisis.
A handout picture released by the Emiri Diwan in Kuwait on July 3, 2017, shows Kuwaiti Foreign Minister Sheikh Sabah al-Khaled al-Sabah (R) receiving Qatari Foreign Minister Sheikh Mohammad Bin Abdulrahman al-Thani at Kuwait International Airport.
Meanwhile, US President Donald Trump spoke separately to Saudi Arabia's King Salman and Abu Dhabi Crown Prince Sheikh Mohammed bin Zayed al-Nahyan on Sunday to discuss his "concerns about the ongoing dispute" between Qatar and its Gulf neighbours.
"We are anxious 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.
On Wednesday, officials from the four countries will meet in Egypt to discuss additional steps.
The UAE ambassador to Russian Federation has said Qatar could face fresh sanctions if it does not comply with the demands.
"If the Qatari rulers insist on rejecting the demands of the four countries and decide to escalate the situation and scramble for countries with ambitions in the region such as Turkey and Iran, we hope our Sudanese brothers will take a clear stance", he said.
On 20 June, the US State Department says it is "mystified" that Saudi Arabia has yet to produce a clear list of demands.
An official told Reuters that besides the closure of al-Jazeera, there has been a demand to eliminate the Turkish military base in Qatar.
"As for the countries that accuse Qatar of financing terrorism, they have the same problems as Qatar, more so, they are on top of the list in that area, " he said.
Qatar's Foreign Minister Mohammed bin Abdulrahman Al-Thani said the demands were created to not be met.