The four Arab nations leading a boycott of Qatar are no longer insisting it comply with a list of 13 specific demands they tabled last month.
Diplomats from Saudi Arabia, the United Arab Emirates, Bahrain and Egypt told reporters at the UN they now wanted it to accept six broad principles.
These include commitments to combat terrorism and extremism and to end acts of provocation and incitement.
There was no immediate comment from Qatar, which denies aiding terrorists.
It has refused to agree to any measures that threaten its sovereignty or violate international law, and denounced the “siege” imposed by its neighbours.
The restrictions put in place six weeks ago have forced the gas-rich emirate to import food by sea and air to meet the basic needs of its population of 2.7 million.
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”.
Frank Gardner, BBC security correspondent
This latest development does, on the surface, hint at a possible way out of the current standoff between Qatar and its neighbours. But it is unlikely to provide a permanent solution.
The problem comes down to how countries choose to interpret “extremism and terrorism”. Qatar has long prided itself on giving voice to alternative views to the edited, government-approved ones aired by its conservative neighbours. Hence one of the reasons why Qatar’s Al Jazeera network has been such a thorn in their sides.
However, the charge levelled against Qatar is that those alternative voices include people committed to the overthrow of governments in the region.
Qatar supports the Muslim Brotherhood, which it considers a peaceful, political force. But Qatar’s opponents in the region consider the Brotherhood to be a terrorist organisation that is an existential threat to their rule. These differences have yet to be resolved.
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”.
Also on Tuesday, NBC News cited US intelligence officials as disputing a report that alleged Qatar had paid a ransom of $1bn (£770m) to Iraqi Shia Muslim militias, Iranian security officials and Sunni Muslim jihadists in Syria as part of a deal to secure the release of royal family members kidnapped in Iraq.
The officials said Qatar had handed €300m ($345m) in cash to Iraq’s government but that Baghdad had confiscated the money after securing the hostages’ release.