RNA - Militants and foreign mercenaries armed by Saudi Arabia and the United Arab Emirates are attempting to capture the well-defended city and push the Houthis out of their sole Red Sea port in the biggest battle of the war.
"A battle of attrition awaits the Saudi alliance which it cannot withstand. The Saudi coalition will not win the battle in Hudaydah," Houthi spokesman Mohammed Abdulsalam told Lebanon-based al-Mayadeen TV.
Saudi Arabia on Sunday conducted airstrikes on the airport, to support forces attempting to seize it. The official SABA news agency said warplanes carried out five strikes on Hudaydah - a lifeline to millions of Yemenis.
Ground troops including Emiratis, Sudanese and Yemenis have surrounded the main airport compound.
Mohammed al-Sharif, deputy head of Yemen's civil aviation, said images circulated online about the airport had been taken in October 2016.
A fence shown as proof of the airport's capture is actually situated near the al-Durayhimi district, on a piece of land belonging to a Yemeni lawmaker, the official Saba news agency quoted him as saying.
Ahmed Taresh, the head of Hudaydah airport, also denied news of the airport's capture, but said that it has been completely destroyed in airstrikes conducted by the Saudi-led coalition.
Abdulsalam warned that the Saudi-UAE offensive against the port city would undermine chances for a peaceful settlement of the Yemen crisis.
The rebuttals came after the media office of the Saudi-backed Yemeni forces loyal to ex-president Abd Rabbuh Mansur Hadi said on Twitter that they had "freed Hudaydah international airport from the grip of" the Houthis.
Reports on Sunday said Saudi-backed forces had been surrounded in the al-Durayhimi Bayt al-Faqih district and at least 40 Saudi mercenaries killed by Yemeni sniper fire over the past two days.
Al-Mayadeen, meanwhile, cited informed sources as saying that the invading forces had retreated from all fronts in Hudaydah's west.
A Yemeni military source said clashes had left 50 Saudi-backed forces dead and destroyed 13 of their armored vehicles in southern Hudaydah.
Yemeni forces have also managed to confiscate a French or American ship off Hudaydah's coast, president of the Houthi Revolutionary Committee Mohammed Ali al-Houthi tweeted.
The UAE, a key member of the Saudi-led coalition waging the war on Yemen, launched the Hudaydah assault on Wednesday despite warnings that it would compound the impoverished nation's humanitarian crisis.
Le Figaro newspaper on Saturday reported that French special forces were present on the ground in Yemen supporting the operation.
According to the Houthis, British and French warships were also on standby on Yemen's western coast to launch missile and aerial attacks on Hudaydah.
Fighting on Saturday closed off the city's northern exit, blocking a key route east to Sana'a and making it harder to transport goods from Yemen's biggest port to mountainous regions.
According to Press TV, the UN World Food Program and the World Health Organization have both expressed concern over the situation.
More than 70 percent of Yemeni imports pass through Hudaydah's docks and the fighting has raised fears of a humanitarian catastrophe in a country already teetering on the brink of famine.
On Saturday, the UN envoy for Yemen Martin Griffiths arrived in Sana'a to hold emergency talks on Hudaydah. He was believed to be pushing a deal for the Houthi fighters to cede control of the Red Sea port to a UN-supervised committee.
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