At a briefing for a group of UN correspondents in New York on Tuesday, diplomats from the four countries said they wanted to resolve the crisis amicably.
Saudi permanent representative Abdullah al-Mouallimi said their foreign ministers had agreed the six principles at a meeting in Cairo on 5 July and that they “should be easy for the Qataris to accept”.
They were combating terrorism and extremism, denying financing and safe havens to terrorist groups, stopping incitement to hatred and violence, and refraining from interfering in the internal affairs of other countries, according to the New York Times.
Mr Mouallimi stressed that there would be “no compromise” on the principles, but added that both sides would be able to discuss how to implement them.
The list of 13 demands handed to Qatar on 22 June included shutting down the Al Jazeera news network, closing a Turkish military base, cutting ties with the Muslim Brotherhood and downgrading relations with Iran.
Mr Mouallimi said closing Al Jazeera might not be necessary but stopping incitement to violence and hate speech was essential.
“If the only way to achieve that is by closing down Al Jazeera, fine,” he was quoted by the Associated Press as saying. “If we can achieve that without closing down Al Jazeera, that’s also fine. The important thing is the objective and the principle involved.”
UAE permanent representative Lana Nusseibeh warned that if Qatar was “unwilling to accept core principles around what defines terrorism or extremism in our region, it will be very difficult” for it to remain in the Gulf Co-operation Council.
Qatar has acknowledged providing assistance to Islamist groups designated as terrorist organisations by some of its neighbours, notably the Muslim Brotherhood. But it has denied aiding jihadist groups linked to al-Qaeda or Islamic State (IS).
UAE Minister of State for International Co-operation Reem al-Hashimi said: “At this stage, the ball is in Qatar’s court.”
She added that the US had “a very constructive and very important role to play in hopefully creating a peaceful resolution to this current crisis”.
US President Donald Trump was quick to claim credit for the pressure being placed on Qatar, saying it might mark the “beginning of the end to the horror of terrorism”.
But his Secretary of State, Rex Tillerson, questioned the list of demands, acknowledging that some elements would “be very difficult for Qatar to meet”.
Mr Tillerson conducted several days of shuttle diplomacy in the region last week and signed a memorandum of understanding with Qatar on countering terrorism financing that Ms Hashimi called “an excellent step”.