UN Secretary General Antonio Guterres has warned the destruction of the port could trigger a "catastrophic" situation in a country where 14 million people are at risk of starvation.
"The fighting must stop, a political debate must begin, and we must prepare a massive humanitarian response to avoid the worst next year", he said.
"The offensive to liberate the port city will continue to prevent the rebels from threatening the worldwide navigation in the Red Sea", al-Maliki said in a press conference in Riyadh, aired live by Al Arabiya.
Griffiths, said the statement, reassured the warring sides that the United Nations remained ready to re-engage the parties on a negotiated agreement for Hodeida, which would protect the port and preserve the humanitarian pipeline.
The United States, Britain and France - three of the main arms suppliers to Saudi Arabia - have also called for an end to almost four years of conflict in Yemen, particularly in Hodeida.
He urged all parties to relaunch peace talks, which were abandoned in September.
British Foreign Minister Jeremy Hunt met Saudi King Salman in Riyadh on Monday to discuss cease-fire in Yemen, according to Saudi-run Al Arabiya television.
Saudi Arabia is leading the Arab military coalition that intervened in Yemen in March 2015 to support the government of President Abd-Rabbu Mansour Hadi after the Houthi rebels forced him into exile.
'The human cost of war in Yemen is incalculable, ' Hunt said ahead of his trip.
Aid groups fear for the safety of hundreds of thousands of people living in Hodeida - and for millions of others dependent on its port for what little food and humanitarian aid trickle into impoverished, blockaded Yemen.
Air strikes against the Iran-aligned Houthis' fortifications were halted for more than 12 hours on Monday and street battles, which had been raging for a week on the outskirts of the Red Sea city, trapping civilians and endangering hospitals, died down, residents said.
Four employees in Hodeida port who requested anonymity told AFP that a rebel commander had been killed in the Monday attack.
Sources at the Al Alfi military hospital, seized by the rebels during their 2014 takeover, said charred body parts had been delivered there overnight.
The port s deputy director, Yahya Sharafeddine, said the main entrance to the docks had been "the target of air raids" but was fully functioning.
Almost 10,000 people have been killed since the coalition joined the conflict in 2015 to bolster President Abedrabbo Mansour Hadi, triggering what the United Nations calls the world's worst humanitarian crisis.
Almost 600 people have been killed since clashes erupted on November 1 in Hodeida, one of Yemen's most densely populated cities.
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