DUBAI, July 9 (Reuters) -

A Saudi-led coalition has made no major gains in its offensive to wrest control of Yemen's Hodeidah port from the Iran-aligned Houthis, leaving it without the decisive increase in leverage it had sought against the group in U.N.-sponsored peace efforts.

The alliance led by Saudi Arabia and the United Arab Emirates launched the offensive on the heavily defended Red Sea city on June 12 in the largest battle of the three-year war, which the United Nations fears risks triggering a famine.

The Arab states pledged a swift operation to take over Hodeidah's air and sea ports, without entering the city center, seeking to minimize civilian casualties and avoid disruption of the port, a lifeline for millions in the impoverished state where 8.4 million are believed to be on the verge of starvation.

But they have made little progress in the campaign which Riyadh and Abu Dhabi say aims to cut off the Houthis' main supply line and force the group to the negotiating table.

The coalition announced on June 20 that it had seized Hodeidah airport, but local military and aid sources told Reuters that neither side has complete control of the airport and its surrounding area, which spreads over 20 km (12 miles).

"The coalition never took control of the airport," Houthi leader Mohammed Ali al-Houthi told Reuters.

A pro-coalition Yemeni military source said the Houthis hold the northern outskirts of the area while coalition-backed forces are trying to maintain their positions along the southern edges.

A senior aid official said coalition forces had initially penetrated the perimeter of the airport. "But that was short lived for less than 24 hours and they were pushed out," the official, who spoke on condition of anonymity, told Reuters.

Coalition spokesman Colonel Turki al-Malki reiterated that the airport was now under the control of the alliance although Houthi fighters continued to launch "indirect fire" from surrounding areas into the airport.

"The coalition is in full control of the airport. There are no Houthi fighters within the airport perimeter," he told Reuters on Monday.

A UAE official said Malki's statement represented both countries.

DAUNTING CHALLENGE

The situation illustrates the daunting challenge faced by the coalition in seeking to take control of Hodeidah port in the absence of a political solution.

The Houthis, who control the most populated areas of Yemen including the capital Sanaa, are adept at guerrilla warfare. Houthi fighters have been harassing UAE-led forces near the airport and on the coastal road that the coalition uses to resupply its forces from military bases on the western coast.

After the UAE announced a halt in military operations to give U.N. mediation efforts a chance, fighting broke out on Friday and Saturday as coalition-backed forces tried to push Houthi fighters further inland to secure the coastal strip south of Hodeidah.

"It's hard to see that the Houthis would be swiftly defeated in Hodeidah, even if the coalition activates what it refers to as local resistance," said Joost Hiltermann, Middle East and North Africa Program Director for International Crisis Group.

The Western-backed alliance intervened in Yemen in 2015 to restore the internationally recognized government in exile, but neither side has made much progress in the conflict, widely seen as a proxy war between Saudi Arabia and archfoe Iran.

U.N. special envoy Martin Griffiths has been shuttling between the warring parties to avert an all-out assault on Hodeidah that the United Nations fears will exacerbate what is already the world's most urgent humanitarian crisis.

He held a second round of talks with the Houthis in Sanaa last week and is expected to do the same with ousted President Abd-Rabbu Mansour Hadi, currently based in his government's temporary headquarters in the southern city of Aden.

The Houthis have offered to hand over management of the port to the United Nations as part of an overall ceasefire in Hodeidah province, according to the United Nations, but the coalition has said that the Houthis must quit the western coast.

The Arab states accuse the Houthis of using the port to smuggle Iranian-made weapons, including missiles that have targeted Saudi cities. Tehran and the group deny the accusations.