"Today, the GCC is suffering from a sort of complete paralysis," he said, adding that despite US President Donald Trump's efforts, blockading countries have not responded positively.
Friday's meeting took place on the sidelines of the United Nations General Assembly and was the first gathering of its kind since Saudi Arabia, the United Arab Emirates, Bahrain, and Egypt severed diplomatic and trade ties with Qatar on June 5, 2017.
The blockading quartet accuses Qatar of having close ties to regional rival Iran and harbouring "terrorism" - allegations Doha strongly denies.
Al Jazeera's Hashem Ahelbarra, reporting from New York, said the move was "quite significant" since it was the first time all parties met face to face over the issue.
US Secretary of State Mike Pompeo spearheaded the talks.
"The idea behind this meeting is that the Americans are trying to build some sort of regional alliance, an 'Arab NATO', to contain what the US sees as Iran's growing influence in the region," Ahelbarra said.
Among things discussed were the strengthening of military ties, as well as economic and diplomatic relations.
Pompeo said earlier this year during a visit to Saudi Arabia that "Gulf unity is necessary and we need to achieve it".
'Productive' meeting
In a separate interview with Al Jazeera, Sheikh Mohammed bin Abdulrahman Al Thani praised the US for leading the meeting.
Saudi Arabia's Foreign Minister Adel al-Jubeir said at the UN General Assembly earlier this week the blockading nations could wait decades for Doha to meet their controversial list of demands.
When asked for Qatar's response to the remarks, Sheikh Mohammed replied: "We have to address the challenges in our region first.
"A year from now, no one will know what the future of the countries will be… Qatar can also wait forever," he added.
"Diplomacy means communication and engagement, and this is Qatar."
At his press conference, Sheikh Mohammed backed the idea of a coalition based on "clear-cut strategies and a road map" to ensure a solid implementation of the initiative.
Sheikh Mohammed noted for the initiative to succeed, there must be certain criteria in place, and a solution to the ongoing GCC crisis. This includes an end to the "illegal procedures" imposed on the Qatari people.
"We were frank and open. We don't need an initiative that will die soon. We want a strong, solid, sustainable one," he said.
Qatar's foreign minister went on to thank US President Donald Trump on his efforts to resolve the crisis.
"The US reaffirmed its commitment to a united GCC, they want a GCC to operate together and more effectively," he said.
Middle East conundrum
Ahelbarra noted the challenges facing the United States, which wants the parties to agree on a number of regional issues including the conflicts in Syria and Yemen.
"How can you bring together all of these people when they defer on every regional conflict," Ahelbarra said.
"Unless you have all the parties agree, I don't see how the Americans can build a regional alliance to contain all the problems in the region," he said.
The US State Department said the ministers agreed on the need to confront threats from Iran and had productive discussions on setting up what is to be known as the "Middle East Strategic Alliance" to promote security and stability in the region.
The GCC is a political and economic alliance of six countries in the Arabian Peninsula: Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.
Before the crisis, citizens of the GCC enjoyed a great deal of freedom of movement between the six member states, but that ended with the blockade.
With close tribal ties, over generations thousands of intermarriages have been celebrated between Qataris and other GCC nationals, and those families are no longer able to see each other.
