He accused the Houthis of seeking to destabilize Saudi Arabia and threaten regional and worldwide security, stating that firing ballistic missiles at residential areas was a violation of global Humanitarian Law.
Though there has been some suggestion that the Houthis could give the port city to the United Nations to administer, avoiding it either being attacked or the port closed to humanitarian aid.
UN Secretary-General Antonio Guterres said there were "intense negotiations" by his UN envoy Martin Griffiths on the fate of the port. The U.N.is also pushing the militants to turn over arms in exchange for an end to the bombing campaign and a transitional governance deal.
Mr Griffiths held several rounds of talks last week in the Yemeni capital of Sanaa, which is held by the rebels.
Yemen's Defense Ministry declared Monday that 250 fighters of the Shiite Houthi group were killed in battles with government forces in the country's western coast areas.
Aid agencies say it is the city's location on the Red Sea that makes it such a strategic prize.
Iran-backed Huthi rebels have in recent months ramped up missile attacks against neighbouring Saudi Arabia, which leads a military coalition that has fought the insurgents since 2015.
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Riyadh and Abu Dhabi however maintain that the port is being used to smuggle weapons. United Nations staff operating out of the port ae already being withdrawn, anticipating the calamity to come.
"It's also our plan and intention to stay and deliver", Lowcock said.
The UN pulled all of its global staff out of Al Hodeidah early on Monday morning. In this regard, he said as much as 5,750,000,000 Yemeni Riyals equivalent to more than $22 million as well as 5297 counterfeited passports were confiscated as they were being sent to the Houthi militias in Saada. "It is essential for him to be given the time that he needs to facilitate a negotiated solution that avoids conflict in the city and we support his efforts to do so".
US Secretary of State Mike Pompeo on Monday called on all parties "to honour their commitments to work with the UN".
"I have spoken with Emirati leaders and made clear our desire to address their security concerns while preserving the free flow of humanitarian aid and life-saving commercial imports", he said.
The three-year conflict has killed more than 10,000 people and displaced more than 3 million.