The five days of talks, which represented the highest-level, public negotiations with the Houthis in the kingdom, come as Saudi Arabia tries a renewed bid to end the yearslong coalition war it launched on Yemen.

That conflict had become enmeshed in a wider regional proxy war the kingdom faced against its longtime regional rival Iran, with which it reached a détente earlier this year.

The Saudi Foreign Ministry in a statement early Wednesday marking the end of the Houthis' trip “welcomed the positive results of the serious discussions regarding reaching a road map to support the peace path in Yemen.”

“The kingdom continues to stand with Yemen and its brotherly people and ... encourages the Yemeni parties to sit at the negotiating table to reach a comprehensive and lasting political solution in Yemen under the supervision of the United Nations," the statement read.

The Houthi delegation even met with Saudi Arabia's defense minister Prince Khalid bin Salman, the brother of the powerful Crown Prince Mohammed bin Salman, during their visit.

In a social media post, Prince Khalid referred to those visiting him as the “Sanaa delegation,” not using either the Houthis nor the rebel group's formal name, Ansar Allah.

“I emphasized the kingdom’s support for Yemen and reaffirmed our commitment to promoting dialogue among all parties to reach a comprehensive political solution under UN supervision,” Prince Khalid said.

Mohammed Abdul-Salam, the chief Houthi negotiator, wrote online that the rebels “held extensive meetings with the Saudi side in which we discussed some options and alternatives to overcome disagreements that previous rounds touched upon.”

“We will submit them to the leadership for consultation and in a way that will help in speeding up the disbursement of salaries and addressing the issues of the humanitarian situation that our Yemeni people are suffering from, leading to a just, comprehensive and sustainable solution," Abdul-Salam said.

The Houthis long have demanded the Saudi-led coalition pay salaries of all state employees under its control — including its military forces — from Yemen's oil and gas revenues, as well as open all airports and ports under Houthi control as part of any peace deal.

The rebel-controlled SABA news agency acknowledged the delegation's return to Sanaa, without elaborating on the talks.

Officials at the United Nations, which is now hosting the annual General Assembly in New York drawing world leaders, did not immediately comment on the Saudi remarks.

A joint statement issued by the United States and the foreign ministers of the Gulf Cooperation Council, a six-nation Gulf Arab bloc led by Riyadh, commended “Saudi Arabia’s sustained efforts to encourage Yemeni-Yemeni dialogue.”

“The ministers also emphasised their support for an inclusive, Yemeni-Yemeni political process under UN auspices that durably resolves the conflict,” that statement read.

US Secretary of State Antony Blinken also met with the foreign ministers of Saudi Arabia and the United Arab Emirates on ending the war on the sidelines of the UN summit.

“We are, in our judgment, in a moment of opportunity, opportunity to help the people of Yemen chart a path toward a durable peace and durable security,” Blinken said.

Yemen’s conflict began in 2014 when the Houthis seized Sanaa and much of the country’s north. The internationally recognized government fled to the south and then into exile in Saudi Arabia.

The Houthi takeover prompted a Saudi-led coalition to intervene months later and the conflict turned into a regional proxy war between Saudi Arabia and Iran, with the United States long involved on the periphery, providing intelligence assistance to the kingdom.

However, international criticism over Saudi airstrikes killing civilians saw the US pull back its support. But the US is suspected of still carrying out drone strikes targeting suspected members of Yemen’s local al-Qaida branch.

The war has killed more than 150,000 people, including fighters and civilians, and created one of the world’s worst humanitarian disasters, killing tens of thousands more.

A cease-fire that expired last October largely has held in the time since, however. Saudi Arabia, its local allies and the Houthis conducted a prisoner exchange in April as part of peace talk efforts.