Impoverished Yemen has remained wracked by violence since 2014, when the Houthis - from their historical stronghold in the northern Saada province - overran much of the country, including capital Sanaa.
The newly appointed United Nations envoy to Yemen, Martin Griffiths, speaks to reporters upon his arrival at Sanaa airport in Sanaa, Yemen, March 24, 2018.
"At every step along the way the Houthis will be given opportunities to retreat, to disarm and to come back to the negotiating process", she said. So far, strategic areas have been liberated and retaken from the rebels.
They say they will attempt to keep the port running and can ease the crisis once they seize it by lifting import restrictions they have imposed. The council also voiced deep concern about the risks to the humanitarian situation in Yemen.
The council "urged all sides to uphold their obligations under global humanitarian law".
Nevertheless, the United Nations envoy for Yemen, Martin Griffiths, has continued to hold talks on keeping Hodeidah open and has urged all sides to exercise restraint.
Mr Griffiths is expected to brief the council on Monday, including on his proposals to restart negotiations to restore peace.
Council members reaffirmed "their full support" for Griffiths' efforts.
The UN considers the Yemeni civil war to be the world's worst humanitarian disaster at present.
The fighting comes at a time when Muslims around the world are celebrating the Eid al-Fitr holiday at the end of the holy month of Ramadan. The Saudi-led coalition entered the conflict in March 2015 and has faced criticism for a campaign of airstrikes killing civilians and destroying hospitals and markets.
Earlier this week, Hadi visited Abu Dhabi's powerful crown prince, Mohammed bin Zayed Al Nahyan.
In a statement, he held the United States and Britain responsible for the Saudi-backed attack on the vital port city. The injured are taken to hospitals in Khoukha, Mocha and Aden, the medical official said.
The main port city of Hodeidah is now under control of Saudi-led coalition forces.
Coalition spokespeople said 18 air attacks were fired on the outskirts of Hudaida on Wednesday.
Forces from an alliance of Arab states fought their way to the outskirts of the airport in Yemen's main port city on Friday, as the Eid holiday saw a battle the United Nations fears could trigger a starvation imperilling millions of lives. The rebels have been raining ballistic missiles down on Saudi cities from across the border.
The Pentagon would not say Thursday whether it had rejected the request for support but called Hodeidah "critical to the delivery of humanitarian assistance to relieve the suffering of the Yemeni people".
Fighting raged near Hudaida airport and al-Durayhmi, a rural area 10km south of the city, UAE's WAM news agency said. "No direct attacks have been reported within Hodeida city itself, despite the overhead presence of fighter jets".
Fighting on the ground is focused on the area around Hodeidah's airport, to the south of the city, and the United Nations reported that aid shipments continued to flow at Hodeidah's port.
Two Saudi and UAE aid ships were in the waters off Hudaida; coalition spokesman Turki al-Maliki told Saudi state media.
The officials declined to give death toll. The official said UAE intelligence indicated that Houthis had mined the port.
It was the second day of an offensive to capture the strategic harbour which is the main entry point for food in a country teetering on the brink of starvation.
A fresh Saudi airstrike on Yemeni city of Sa'ada has killed seven civilians including a woman.
SABA reported late Wednesday the forces captured the town of Nakhilia in the district of ad-Durayhimi about 20 kilometers (12.5 miles) south of Hodeida International Airport.
Huthi urged his troops to "confront the forces of tyranny", warning they would recapture areas taken by pro-government forces by bringing "huge numbers" of fighters to the battle, according to the rebels' Al-Masirah TV. Instead, he suggested, coalition forces would focus on taking the airport, the seaport and the road to the Houthi capital at Sanaa.
Forces advancing on the ground approached the Hodeidah airport, while ambulances wounded a number of the Saudi-backed invading forces wounded in the fighting.