UNITED NATIONS -- Kuwait, acting as a mediator in a snowballing international spat, presented Qatar on Friday with a list of demands from Saudi Arabia, Bahrain, the United Arab Emirates and Egypt, four Arab nations that severed ties with Qatar in early June.

A copy of the list obtained by The Associated Press shows the four countries are demanding, among 13 points in total, that Qatar restrict diplomatic ties with Iran, close a Turkish military base on its territory, severe ties with the Muslim Brotherhood, and shutter the Al-Jazeera broadcasting network. CBS News has confirmed that the list of demands, as reported by the AP, is accurate.

The four nations gave Qatar 10 days to meet the demands, but it wasn't clear what actions they might take if Doha failed to comply.

There was no immediate official reaction from the Qatari capital of Doha to the list of demands, but it comes as the Trump administration appears increasingly frustrated by the Saudi-led embargo on the tiny Gulf state, and the inability of the neighboring nations to ease the tension.

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CBS News correspondent Margaret Brennan reports that, as the diplomatic dispute between some of America's closest Middle East allies deepened and Saudi Arabia and the other three nations drafted their list of demands, the U.S. State Department made it clear that Washington was keen to see an expeditious resolution to the crisis.

A spokesperson for the State Department said, in an unusually direct prodding, that the Trump administration was "mystified" as to why it took so long for the UAE and the Saudis to draft the demands, which suggested a political rather than security-based motive behind the diplomatic standoff.

Brennan also noted that the Qatari foreign minister is to be in Washington next week to meet Trump administration officials in an attempt to resolve the dispute. Saudi Foreign Minister Adel al Jubeir met in Washington with Rex Tillerson earlier this week, as the list was being drafted in consultation with the UAE.

In an exclusive interview with CBS News, Qatar's U.N. Ambassador Sheikha Alya Ahmed bin Saif Al-Thani said the allegations that her country supports terrorism are, "sabotaging our relationship with the world, with the West, tarnishing our reputation in a way by using the terrorism card."

"The blockade they have imposed is illegal," Al-Thani insisted. "They used the terrorism card as a way of attracting attention. But the main objectives are more about criticizing our media, Al-Jazeera, and our openness."

"We are small," Al-Thani said, "but we have integrity."

Five years ago, CBS News' 60 Minutes profiled Qatar as a country that had largely avoided the upheaval of the Arab Spring protests. Now, Al-Thani says, Qatar has to defend itself.

In mid-June, Egypt wrote to the United Nations Security Council to request an investigation into what it called "media reports" that Qatar had paid a ransom of $1 billion to a terrorist group in Iraq to release members of its royal family who were kidnapped while on a hunting trip. In the letter, obtained by CBS News, Egypt called the incident, if confirmed, a "clear violation" of Security Council resolutions.

State Department spokesperson Heather Nauert said this week, however, that the current standoff in the heart of the Arab world is the culmination of a "long-simmering" dispute.

James F. Jeffrey, former U.S. Ambassador to Turkey and Iraq who is now a distinguished fellow at the Washington Institute of Near East Policy in Washington, told CBS News the crisis, "was made largely by the Saudis and the Emiratis," but he added that it was, "probably inadvertently encouraged by President Trump."

With U.S. troops deployed to the region, including thousands based in Qatar and playing a vital role in the U.S.-led coalition battling ISIS militants in Syria and Iraq, the result is dangerous.

"You now have split the anti-Iranian and anti-ISIS coalition," Jeffrey said.

"The U.S. is not only trying to mediate this thing, but there is some impatience and concern that the Saudis and the Emiratis are getting ahead of their headlights," Jeffrey told CBS News. "The President has introduced a new factor into this by his tweeting."

"I think we are still getting mixed signals from the Administration, and there is still a good amount of confusion about what U.S. policy is vis-à-vis this rift," Dalia Dassa Kaye, director of the Center for Middle East Public Policy at the RAND Corporation, told CBS News.

Al-Thani insisted that Qatar has been restrained in its response, and in particular, she said, they have not cut the vital natural gas flow that they control to the region. So is there still a threat that they might turn off the gas?

"Of course not," Al-Thani said. "We have been clear on that."

Qatar's Ambassador to the United Nations, Sheikha Alya Ahmed bin Saif Al-Thani, is seen in a photo posted to her official Twitter account. Twitter/Alya Ahmed Al Thani

Last week, Al-Thani handed a letter to the U.N. Secretary General, "updating him on the humanitarian impacts of the blockade, and the illegality of it."

Al-Thani disputes the terrorism claims and says the fact that Qatar has one of the world's largest natural gas reserves, and that it is the first Arab country to host the 2022 FIFA World Championship, have been sources of tension: "For us it's been very clear since day one: Their justifications are baseless."

The dispute pits oil-rich Saudi Arabia and the other Gulf states against gas-rich Qatar.

Analysts say the support for terror argument is murky, and many have noted that support, in the form of cash and arms, has flowed from all the Gulf countries to various armed groups in the region.

"The Saudis and Emiratis each have their reasons for trying to press Qatar back in line, but their clashing priorities and alliances weaken the impact of their threats," Joost Hiltermann, Middle East and North Africa program director for International Crisis Group, wrote.

Jeffrey concedes the point; "The sins of the Qataris are not insignificant, but in terms of supporting radical groups, much of it in Syria, there is not much difference between the groups they supported and the groups that the Emiratis, the Saudis and the Turks have supported."

The rift, says Kaye, "is really an intra-Sunni rift, and it has a lot more to do with differences about the future ways these countries should be governed and different definitions of who's an extremist."

Jeffrey says he thinks the Saudis "were clearly far too aggressive. They didn't think this thing out and now America has to fix it."

Jeffrey, who advised Secretary of State Rex Tillerson when he was at Exxon, says he believes the U.S. chief diplomat knows the region very well, and is trying hard to calm the situation down by pushing through a deal to sell F-15 fighter jets to Qatar and to organize military exercises with the Qatari Navy.

Al-Thani believes that the Saudi position is softening, but not that of the UAE. She hopes for a resolution, but fears a prolonged chill: "They continue to escalate even though both Kuwait and the United States are playing an important role."

"We are confident of the U.S. position toward the blockade," Al-Thani added.