The official spokesman for the Coalition to Restore Legitimacy in Yemen, Col.
The government and Houthi rebels have been engaged in an armed conflict for more than 3 years.
Griffiths was in Amman following an intense round of shuttle diplomacy this week with Yemen's Huthi rebels, who control the port, Saudi Arabia and the United Arab Emirates, whose forces are backing the Hodeida offensive.
Launching ballistic missiles towards densely populated cities and villages breaches the worldwide humanitarian law, he added.
The United Nations says it remains in Yemen's Red Sea port of Hodeida, the target of a new offensive by a Saudi-led coalition, and is working with aid groups to help those affected by the conflict.
State media in both Saudi Arabia and the United Arab Emirates did not immediately acknowledge the assault. The Saudi-led coalition entered the war in March 2015.
Hodeida is home to 600,000 people and is the entry point for 70 percent of Yemen's imports, including vital aid supplies for civilians in the war-wracked country.
It would be the first time since they joined the war on behalf of Yemen's exiled government that the foreign armies have attempted to capture such a well-defended major city.
"I think the Emiratis have done a good job in presenting compelling arguments about why an operation (on Hodeidah) could in the end tip the balance and apply enough pressure to bring the Houthis to the table", a Western diplomat said on Monday.
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The Houthi-run Al Masirah satellite news channel claimed rebel forces hit a Saudi coalition ship near Hodeida with two missiles.
Russia's U.N. Ambassador Vassily Nebenzia, the current council president, told reporters Wednesday that the United Kingdom asked for the meeting.
Forces loyal to Yemen's exiled government and irregular fighters led by Emirati troops had neared Hodeida in recent days. The sound of heavy, sustained gunfire clearly could be heard in the background.
Griffiths warned in a statement earlier Wednesday that "further military escalation will have serious consequences on the dire humanitarian situation in the country" and hinder his efforts to restart political negotiations.
Emirati Minister of State for Foreign Affairs Anwar Gargash earlier told French newspaper Le Figaro the deadline for a withdrawal from Hodeida by the Houthis expired early Wednesday morning.
Reports over the weekend suggested the Lower Al-Jahah area, south of the city, had been captured in fierce fighting.
Worldwide aid agencies and the United Nations have warned the assault could shut down the vital aid route for some 70 percent of Yemen's food, as well as the bulk of humanitarian aid and fuel supplies.
The aid group Oxfam said humanitarian organizations received warnings over the weekend for staff to evacuate Hodeida by Tuesday ahead of an offensive. It says the lives of 250,000 residents are threatened.