By Tamara Qiblawi

(CNN) -- US Secretary of State Rex Tillerson made an unexpected return to Qatar Thursday, extending his tour of the crisis-embroiled Gulf as the standoff between the gas-rich nation and the Saudi-led quartet showed no signs of abating.

Tillerson was expected to meet with Qatari Emir Tamim bin Hamad Al Thani in Doha, a day after a high-level meeting in Jeddah with foreign ministers from Saudi Arabia, Bahrain, Egypt, Kuwait and the United Arab Emirates.

The quartet has accused Qatar of supporting terrorism, a charge Doha denies.

Speaking at a joint press conference on Wednesday, UAE Minister of Foreign Affairs and International Cooperation Sheikh Abdullah bin Zayed Al Nahyan said Qatar must "double its efforts" to join its gulf neighbors in combating terrorism.

"If Qatar wants to be a member of this alliance then they are more than welcome but if Qatar wants to be on the other side, then as we say in Arabic, it's time to say 'good bye,'" the Emirati minister said, according to the UAE's state news agency.

With no sign of a breakthrough on Wednesday, Tillerson -- who left Jeddah and made an overnight stop in Kuwait -- was expected to share the views he heard in Saudi Arabia with the Emir of Qatar during his Thursday meeting.

On an earlier trip to Qatar this week, the US' top diplomat signed a memorandum of understanding between the US and Qatar on fighting terrorism. In response, the quartet said the sanctions would remain until its full demands were met.

US senator weighs in

Amid Tillerson's shuttle diplomacy, an influential US Republican senator weighed in on standoff at Wednesday's Senate Relations Committee.

Chairman of the US Senate Foreign Relations Committee Bob Corker said on Wednesday he was "really disappointed" by Saudi Arabia's actions after the recent summit of Arab states in the Saudi capital, which marked US President Donald Trump's visit to the country.

"I think possibly this is a rookie mistake by crown prince who I think could be the future of Saudi Arabia," said Corker.

Saudi Crown Prince Mohammed Bin Salman, 31, was appointed to his post last month, less than three weeks after crisis began.

Corker said that Saudi Arabia's "support for terrorism by Saudi Arabia dwarfs what Qatar is doing."

"...I think this is an opportunity for us to call all of them out -- Bahrain, UAE, all of these countries that support terrorism.

UAE: Al Jazeera promotes 'extremist ideologies'

Separately on Wednesday the UAE said it had sent a letter to the United Nations High Commissioner for Human Rights accusing Qatar-backed Al Jazeera of promoting "extremist narratives."

The shut down of the network is on the list of demands from the quartet.

"The letter makes clear that Al Jazeera's reporting has repeatedly crossed the threshold of incitement to hostility, violence and discrimination, and lists several examples of such content," the official press release from the UAE said. The letter cites the Joint declaration on Freedom of Expression and Countering Violent Extremism which stipulates that states may restrict reporting that appears to incite violence.

UN Special Rapporteur on the promotion and protection of the right to freedom and expression David Kaye has called the demand to shut down Al Jazeera "a major blow to media pluralism."

The Al Jazeera Media network has launched a social media campaign to defend the network from "the unreasonable demands presented by the blockading countries to Qatar."

CNN's Sarah Sirgany, Laura Smith-Spark, Nicole Gaouette and Zachary Cohen contributed to this report.

The-CNN-Wire