Yemen's Iran-backed Huthi rebels suffered 30 fatalities in the fighting, which took place 2 km from Hodeida airport, south of the city, medical sources told AFP.
Council members held the emergency closed-door session after the Saudi-led coalition began airstrikes on Hodeida early Wednesday, after what coalition partner the United Arab Emirates said was the expiration of a deadline for Iranian-backed Houthi rebels to surrender the critical Red Sea port.
The closed meeting requested by the United Kingdom comes as residents flee outskirts of city fearing incoming air attacks.
Fighting on Thursday appeared to be concentrated around the city's airport, the first strategic target the Arab coalition is trying to seize before battling for control of the vital port facilities.
"My family left for Sanaa yesterday but I stayed behind alone to protect our home from looters", said Mohammed Abdullah, an employee of the Houthi administration.
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.
Much of the country's food and medical supplies travel through the port city, making the situation even worse for the millions facing starvation.
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Arab diplomats say there are plans in place to prevent the battle from causing a humanitarian disaster, and they will be able to improve food supplies once they control the port.
"The situation is dire and we don't know how it will end", said Khadija, a teacher in Hodeidah.
The port is also a lucrative source of revenue for the Houthis, who control most of Yemen's north since 2014.
A report by the Saudi-owned satellite network Al Arabiya has quoted commander Abu Zarah al-Mahrami as saying government forces are "within meters" of the airport. Aden has served as his government's temporary capital since 2015.
The news agency says fierce battles have raged between government forces and Shiite rebel Houthis in areas on the outskirts of Hodeida.
With logistical support from the USA, the Saudi-led coalition has been carrying out attacks inside Yemen since March 2015, killing at least 10,000 people, in an attempt to reinstate the internationally recognised government of President Abu-Rabbu Mansour Hadi.
France provided minesweeping support at the UAE's request after the U.S. did not want to or was not able to, but it's not clear if the mass assault on Hudaydah received other support in the form of intelligence, surveillance or reconnaissance assets, as the Emirates requested.
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The requests were for aerial satellite imagery, other surveillance and reconnaissance, and minesweeping, said the official, who spoke on condition of anonymity because he was not authorized to publicly discuss the matter.
"We saw the resistance forces in the square at the northwestern entrance to the airport", said a Hodeidah resident, referring to Yemeni allies of the Saudi-led Arab alliance.
In a statement to Reuters, the French Defence Ministry suggested a final decision had not yet been made. The Pentagon declined to comment. The Houthis generate USD30 million to USD40 million a month in revenue from the port, the UAE official estimated.
The United States and other Western powers provide arms and intelligence to the coalition.
The United Nations has warned the military operation could cripple deliveries of commercial goods and humanitarian aid to millions of people in Yemen. Approximately 80 per cent of the country's humanitarian aid enters though the port. "The global community must pressure the Houthis to evacuate Hodeida and leave the port intact".
The Houthi-run Al Masirah satellite news channel aired footage it described as being from near Hodeida showing a burned-out truck, corpses of irregular fighters and a damaged Emirati armoured vehicle.
But the council brushed aside a call by Sweden, a non-permanent member, for a freeze to the military operation to allow time for talks on a rebel withdrawal from the Red Sea port.
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