HRW's Sarah Leah Whitson said Friday "the coalition and Houthi forces, now fighting for Hodeida, have atrocious records abiding by the laws of war".
Residents said battles had been fought in the Manzar neighbourhood abutting the wall around the airport.
"There have been terrifying bombing runs since the morning when they struck Houthi positions near the airport", said fish vendor Ammar Ahmed.
Houthi forces had entered homes overlooking the main road to go onto the roofs.
The closed meeting requested by the United Kingdom comes as residents flee outskirts of city fearing incoming air attacks.
In earlier statements, the army had said that government forces were advancing on the city of Al-Hudaydah after having seized control of the Nakhilah Market roughly seven kilometers from the city's main airport.
The attack was launched on the coastal road that leads up from the government-held towns of Khokha and Mokha.
Thursday marked the first full day of fighting in and around the Yemeni port city of Hodeidah, At least 39 people were killed in the course of this fighting, and a limited amount of territory outside of the city fell to the invading pro-Saudi forces.
In other key findings, the secretary-general said the U.N.is looking into reports from two unnamed countries that Iran received "dual-use items, materials, equipment, goods and technology" in violation of United Nations restrictions.
The government and Houthi rebels have been engaged in an armed conflict for more than 3 years.
"The western coast will turn into a big swamp for the invaders", he added.
Sri Lanka were ready to forfeit St. Lucia Test
In its second innings, Sri Lanka lost Kusal Perera to a thick edge behind off Shannon Gabriel two overs before stumps. In March this year, Australia were caught tampering with the ball in the third Test against South Africa in Cape Town.
The UN official further called on Yemen's warring camps "to meet their obligations to protect civilians and civilian infrastructure and... respect worldwide humanitarian law".
An AFP correspondent south of Hudaida airport reported seeing ambulances evacuating dead and wounded government loyalist fighters as reinforcements headed towards the front line. "We think every time we push hard the Houthis accept to engage, and they will engage more", he said. There was no independent confirmation of the report.
The United Nations is struggling to avert disruption to the port, the main lifeline for food aid to a country where 8.4 million people are on the verge of starvation. "We have to keep that port open, we have to make sure that people get the supplies that they need". The work in the port is normal. "The sea port is totally out of operations today", he told reporters on Thursday.
The Saudi-led coalition backing Yemen's exiled government began the assault on the port city of Hodeida (hoh-DY'-duh) on Wednesday. A halt to this assistance could have a significant effect on the coalition's warfighting capability: among others, ex-CIA analyst Bruce Reidel assesses that the Royal Saudi Air Force is "wholly dependent on American and British support for its maintenance and operations".
Iran has condemned the Saudi-led coalition's assault on the Yemeni port city of Hodeida, which is controlled by rebels aligned with Tehran.
As the conflict enters its fourth year, millions are without access to clean drinking water, and the country is at high risk of a cholera epidemic, Guterres said.
Members of the United Nations Security Council have expressed concern at an emergency meeting about the humanitarian crisis in Yemen regarding an ongoing operation around a key port city.
Though the city's port still seems to be open, CARE said it can't confirm that goods are able to move into the country.
The US has said it supports UN-mediated efforts to resolve the issue.
The UN's envoy for Yemen, Martin Griffiths, was to brief council members by video-conference.
The coalition of Arab states has battled with little success for three years to defeat the Houthis, who control the capital Sanaa, the main port at Hodeidah and most of Yemen's populated areas.
The United States has turned down three requests within the past 24 hours from the UAE to provide more support, including minesweepers. It will be the second time the Council convenes this week over the situation in Yemen, which aid groups warn stares at an imminent humanitarian crisis.