A US -backed, Saudi-led military coalition is fighting against the Houthis on behalf of the government of President Abd Rabu Mansour Hadi, who lives in exile in Riyadh.
All signs early on Tuesday pointed to an imminent offensive on Yemen's coastal city of Al Hodeidah, led by the national Yemeni forces and with support from the Arab coalition to end the Houthi militia control over the city.
"We are doing everything we can through diplomatic channels to discourage an assault on Hodeidah".
Following the closed-door council meeting, Russian Ambassador Vassily Nebenzia, who is council president this month, called for de-escalation and said the top United Nations body would be "closely" following developments.
A pro-government Yemeni soldier fires a machine gun on June 7, 2018, near the city of Al Jah in the Hodeida province, 50 kilometers from the port city of Hodeida, which the Iran-backed Huthi insurgents seized in 2014.
By late today, key lawmakers had begun losing faith in USA efforts to convince Saudi and UAE military officials to stop the assault, after The Wall Street Journal reported that the UN's shuttle diplomacy failed to move UAE officials and that the Donald Trump administration had given the operation "a blinking yellow light".
United Nations aid chief Mark Lowcock, who also briefed the council, said an attack on Hodeida would be "catastrophic" and that aid agencies were hoping to "stay and deliver" in Yemen, which the United Nations describes as the world's worst humanitarian crisis.
"We are, at the present moment, in intense consultation", the UN's secretary general, António Guterres, told reporters. "But we are also anxious about the humanitarian situation".More news: Spain offers to take migrants stranded in Mediterranean Sea
Yemen relies on imports for 90 percent of its food and 70% of those transit through Hodeida, Lowcock said.
Saudi and UAE-backed Yemeni government forces have surrounded the key port of Hodieda in recent weeks, putting pressure on the Houthi defenders.
Eleven humanitarian aid agencies, including Oxfam and Save the Children, separately urged British Foreign Secretary Boris Johnson to threaten to cut off British support to the coalition if it attacks Hodeida.
The United Nations pulled all of its worldwide staff out of Al Hodeidah early on Monday morning.
Saudi Arabia launched a war against the Houthis in March 2015, backing Yemen's internationally recognized government after the rebels drove them from the capital, Sanaa.
The three-year stalemated war has killed more than 10,000 people and displaced more than 3 million.
An alarming 22.2 million people in Yemen - the Arab world's poorest country - need some kind of humanitarian or protection assistance, according to the United Nations Office for the Coordination of Humanitarian Affairs (OCHA).