GENEVA/RIYADH (Reuters) - The Saudi-led military coalition fighting the Houthis in Yemen said on Friday it would welcome a political deal to end the conflict but indicated it would keep insisting on a complete withdrawal by the Houthis from territory seized since 2014.

FILE PHOTO - UN envoy to Yemen Martin Griffiths listens to the undersecretary of Houthi-led government's foreign ministry, Faisal Abu-Rass (not pictured) upon his departure of Sanaa, Yemen June 19, 2018. REUTERS/Khaled Abdullah

The statement from the alliance came after U.N. Yemen envoy Martin Griffiths said he hoped to get the warring parties to the negotiating table in the next few weeks to end fighting at the port city of Hodeidah, a lifeline for Yemen.

The United Nations hopes a breakthrough at Hodeidah could lead to a wider solution to the three-year-old conflict that has killed more than 10,000 and caused the world’s most urgent humanitarian crisis, with millions facing starvation and disease.

“I’d like to get the parties together within the next few weeks at the very latest,” Griffiths told U.N. radio late on Thursday. “I’m hoping that the (U.N.) Security Council will meet next week and we’ll put a plan before them as to how we’re going to bring the talks back.”

In recent days Griffiths met ousted President Abd-Rabbu Mansour Hadi and with Mohammed Abdul-Salam, chief negotiator of the Houthi group, which controls the capital Sanaa and most populated areas.

The alliance of Arab states led by the UAE and Saudi Arabia has been fighting since 2015 to restore Hadi’s government and describes the Houthis as pawns of Iran, accusations the Houthis and Tehran deny.

“Both parties have confirmed to me their willingness to come to the table to restart negotiations. I think it’s long overdue that that should take place,” Griffiths said.

The Houthis have offered to hand over management of Hodeidah port to the United Nations as part of an overall ceasefire in the governorate and Griffiths said he expected further talks with the Houthis in the coming days to agree on timing and other details.

Hadi’s side has accepted the proposal but efforts to avert an all-out attack on the port facilities were continuing, the U.N. envoy said.

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The Houthis have so far not yielded any territory they seized willingly. U.N. talks on a political deal collapsed in 2016 when Hadi’s government walked out after the Houthis refused to quit Yemen’s three main cities, including Sanaa and Hodeidah.

The Riyadh-led coalition fighting to restore Hadi’s government said in a statement issued after Griffiths’ comments that “a political deal remains the best and most adequate solution to get Yemen out of its crisis.”

However, it said any peace deal should respect previous initiatives including a U.N. Security Council resolution on Yemen, all of which demand a Houthi withdrawal from territory seized since 2014.

The United Arab Emirates, which has been overseeing the Hodeidah offensive, has said repeatedly that any deal would have to include the condition that the Houthis leave the port city and all its other territory on Yemen’s coast.

The Houthis were not immediately available for comment. The group has previously said it would not withdraw from Hodeidah.

On Friday, the frontlines were almost silent, military sources and residents of Hodeidah province told Reuters, in a possible sign that Griffiths’ efforts may have started to bear results.

“Coalition forces were more focused in the last two days on securing the coastal road and consolidating previous gains,” one Yemeni military said.

“Except some skirmishes, it has been very calm all around Hodeidah airport,” the source added.

The international community fears the next phase of the battle could see the Saudi-led coalition and its forces attack the city center and move on the port, which could cause both high casualties in Hodeidah itself, and a potential humanitarian catastrophe if supplies to the rest of Yemen are cut.

The Houthis have been preparing for battle inside Hodeidah by digging trenches, building defense berms and reinforcing their ranks with troops in Hodeidah and in other towns surrounding the city.