The statement came after foreign ministers from Egypt, Saudi Arabia, the United Arab Emirates and Bahrain - the Arab states involved in the dispute with Qatar - met in Egypt's capital after receiving Doha's response to their list of demands.
Qatar Airways said on Thursday that passengers travelling to the USA can now carry their laptops and other large electronics on board, ending a three-month in-cabin ban on devices for the Doha-based airline.
Egyptian Foreign Minister Sameh Shoukry said the four countries reiterated the necessity to combat terrorism and to dry up its sources.
"They are constrained in what escalation measures they can take and they're facing an global community that prefers some kind of negotiated settlement, which they're not really interested in, " Griffiths said.
"Qatar will never do", Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani said.
Saudi Arabia and the UAE used it to launch what the Qatari foreign minister called an unjustified blockade.
The states arrayed against Qatar later presented Doha with a list of 13 demands, which they said must be met before the embargo is lifted.
That is why Qatar enjoys strong support of Turkey, the most powerful North Atlantic Treaty Organisation country in the region.
Saudi's Foreign Minister Adel al-Jubeir highlighted that they will "take the right steps at the right time" without going into details while stressing that "Qatar must change its policies for our stance to change".
On June 5, Saudi Arabia, Egypt, the UAE, Bahrain and Yemen all abruptly cut diplomatic ties with Qatar, accusing it of meddling in their domestic affairs and supporting terrorist groups.
"To this end, closer cooperation between the two countries' secret services was agreed during Foreign Minister Sigmar Gabriel's visit to the Gulf emirate", a source in the German delegation to Qatar told the Die Zeit newspaper.
The countries in question claimed that Qatar supports terrorist groups such as ISIS ("Islamic State in Iraq and Syria"), al-Qaeda, and the Muslim Brotherhood as well as the Houthi Shiite rebels in Yemen, and that Qatar threatens their national security.
"Qatar has not taken counter-measures, has not considered how it can attack the other countries in a similar way, economically or politically, but from the first minute has tried to ask for dialogue", Gabriel said.
The Saudi-led alliance has "plenty of cards to play", including more financial sanctions, but none of the options are "painless things to do", said David Andrew Weinberg, a senior fellow at the Foundation for Defense of Democracies.
Ahead of the meeting to discuss Qatar's response, USA president Donald Trump spoke with his Egyptian counterpart Abdel Fattah El Sisi and "called on all parties to negotiate constructively to resolve the dispute", the White House said.