Fighter jets from the Saudi-led Arab coalition pounded coastal areas south-east of the city on Friday as residents gathered at dawn in an open area for Eid Al Fitr prayers, Reuters reported.
Saudi Arabia, the United Arab Emirates and other allies intervened in Yemen in 2015 to push back the rebels and restore the internationally recognized government to power after the Houthis ousted it from swathes of the country including the capital Sanaa.
The Houthis suffered 30 fatalities yesterday in clashes near Hodeida airport south of the city, medical sources told AFP.
But a successful operation would require swiftly capturing a city of 600,000 people, without inflicting damage that would destroy the port.
Their fear is that a protracted fight could force a shutdown of Hodeida's port at a time when a halt in aid risks tipping millions into starvation.
The United States rejected a request from the UAE for intelligence, mine-sweeping and airborne intelligence, surveillance and reconnaissance (ISR) assets for the Hudaida operation, a UAE official said, speaking on condition of anonymity, while noting congressional opposition.
Despite an worldwide arms embargo against the rebels, the coalition accuses them of using the port to smuggle weapons into the country, a charge the Houthis deny.
David Greene talks with United Nations humanitarian coordinator in Yemen Lise Grande.
Two Saudi and UAE aid ships were in the waters off Hodeidah, coalition spokesman Turki al-Maliki told Saudi state media.
"Any closure of the port, even for a few days, will have a dramatic impact on the humanitarian operations in the country", the U.N. Humanitarian Coordinator for Yemen, Lise Grande, told The Associated Press Thursday.
Tribal fighters loyal to the Yemeni government stand by a tank in al-Faza area near Hodeida, Yemen June 1, 2018.
Ahead of the talks, Swedish UN ambassador Carl Skau said it was time for the council to call for an immediate freeze to the military operation.
The council made the call following United Nations warnings of a looming humanitarian disaster from the assault. And urban fighting could put countless civilian lives at risk, displace hundreds of thousands of people and disrupt efforts to alleviate Yemeni suffering.
"The liberation of Hodeidah is the cornerstone of overthrowing the financial empire built by Houthis", said Ibrahim, another Sanaa citizen.
Global aid agencies and the United Nations have warned the assault could shut down the vital aid route for some 70 per cent of Yemen's food, as well as the bulk of humanitarian aid and fuel supplies. Ambassador Vasily A Nebenzia of Russian Federation, the 15-member council's president for June, told reporters that it "urged all sides to uphold their obligations under worldwide law".
The Saudi-led coalition has imposed an air, sea, and land embargo on Yemen since March 2015, aiming to dislodge the Houthis from cities they control, paralyzing trade and access to the country.
The UN and Western nations have accused Iran of supplying the Houthis with weapons, from assault rifles to the ballistic missiles they have fired deep into Saudi Arabia, including at the capital Riyadh.
The UN has warned against an offensive on Hodeidah because the port serves as the entry point for 70 percent of Yemen's imports, with the country already teetering on the brink of starvation after three years of war.
The Houthis deployed military vehicles and troops in the city centre and near the port, as warplanes struck the coast to the south, residents said.
The call from Human Rights Watch comes as a Saudi-led coalition tries to retake the port city of Hodeida from Shiite rebels known as Houthis.
Saudi Arabia's official Al-Arabia net reports that the Yemeni army (loyal to Hadi government) announced on Thursday that it has advanced and reached the surroundings of the Hudeidah Airport.
An administration official acknowledged that the coalition would like the U.S.to get more involved militarily in the battle to free the port, but so far that has not happened.