By Aziz El Yaakoubi and Maha El Dahan
RIMBO, Sweden/ADEN (Reuters) - Yemen's warring parties agreed on Wednesday to reopen Sanaa airport in the Houthi-held capital, sources said, as Western nations pressed the two sides to accept confidence-building steps before the end of U.N.-led peace talks in Sweden.
The Iranian-aligned Houthi movement and the Saudi-backed government of Abd-Rabbu Mansour Hadi were still discussing a United Nations proposal on the contested port city of Hodeidah, a lifeline for millions of Yemenis facing starvation.
Hadi's premier, Maeen Abdulmalik Saeed, told reporters in the government's base in the southern port of Aden that there might not be enough time for full agreement on Hodeidah as the talks, the first in over two years, conclude on Thursday.
"We talked about (it) a lot but with the limited time we have, we can’t talk about all the points in this round. The important thing is to build confidence and then go into the details of the Hodeidah file," he said.
U.N. Secretary-General Antonio Guterres is due to attend the final day of talks to support his envoy's efforts to launch a political process to end the nearly four-year-old war. Another round of talks could be held in early 2019.
The Houthis hold most population centres, including Hodeidah and Sanaa from which it ousted Hadi's government in 2014.
A U.N. spokeswoman said both parties had received a "final package" of agreements on the status of Hodeidah, Sanaa airport, a political framework and shoring up the economy. "We hope to receive positive responses," she said.
The two parties agreed that international flights would stop at a government-held airport for inspections before flying in or out of Sanaa, two sources familiar with the talks said.
They have yet to agree on whether those inspections would be in Aden airport or that of Sayun, the sources added.
The Saudi-led military coalition that intervened in the war in 2015 to restore Hadi's government controls Yemen's air space.
The coalition has faced increased scrutiny from Western allies, some of which supply it with arms and intelligence, over the war that has killed tens of thousands of people.
Ambassadors from countries that are permanent members of the Security Council have joined talks with delegation chiefs.
U.S. President Donald Trump told Reuters on Tuesday he could abide by legislation to end U.S. support for coalition forces in the war following outrage over the murder of Saudi journalist Jamal Khashoggi.
"I hate to see what's going on in Yemen," Trump said. "But it takes two to tango. I'd want to see Iran pull out of Yemen too."
The conflict is seen in the Middle East as a proxy war between Saudi Arabia and Iran, which welcomed peace efforts.
Asked about the U.S. Senate deliberations, Saeed said Yemen's stability was important for regional security: "The U.S. cannot overlook what Iran is doing in Yemen."
U.N. envoy Martin Griffiths, trying to avert a full-scale assault on Hodeidah, where coalition forces have massed on the outskirts, is asking both sides to withdraw from the city.
His proposal envisions an interim entity being formed to run the city and port and international monitors being deployed.
Both sides have agreed to a U.N. role in the port, the entry point for most of Yemen's commercial imports and vital aid, but differ on who should run the city. The Houthis want Hodeidah declared a neutral zone, while Hadi's government believes the city should fall under its control as a matter of sovereignty.
"The devil is in the details - withdraw how far (from Hodeidah), the sequence, who governs and delivers services," said one diplomat, speaking on condition of anonymity.
The sides have also yet to agree on shoring up the central bank, and on a transitional governing body, although a deal was struck on a prisoner swap that could see 15,000 prisoners freed.
A small group of Yemenis demonstrated outside the talks venue in Rimbo, north of Stockholm, waving the flags of former South Yemen in support of a separatist movement that is fighting alongside the coalition while trying to undermine Hadi's government.
(Additional reporting by Mohammed Ghobari in Aden and Steve Holland and Roberta Rampton in Washington; Writing by Ghaida Ghantous; Editing by Hugh Lawson and Mark Heinrich)