The Saudi-led coalition faces widespread global criticism for its airstrikes in Yemen that kill civilians.
The council met behind closed doors to hear United Nations envoy Martin Griffiths report on his diplomatic efforts to keep the rebel-held port of Hodeida open to shipments of aid and commercial goods.
"There is a humanitarian cost to liberate #Hodeidah, but if the city remains under the control of the Iranian-backed #Houthis militias that's will result in a higher cost for sure".
Urgent British-led efforts at the UN were under way to dissuade the United Arab Emirates and the Saudis from pressing ahead with the attack - or at least to give undertakings that it will not seek to starve Hodeidah into submission.
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.
The Western diplomat said there were "a couple of last ditch attempts" to try to see whether there were any options to de-escalate, including a plan to "see some sort of a temporary ceasefire", but that would involve the Houthis putting their weapons down or potentially even moving out of the port.
Nearly 10,000 people have been killed since the alliance launched its intervention, contributing to what the United Nations has called the world's worst humanitarian crisis.
"We are, at the present moment, in intense consultation", Guterres told reporters on Monday.
United Nations humanitarian chief Mark Lowcock told reporters today that 70 percent of Yemen's imported food, fuel, and medicines come through Hodeidah.
"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.
UN Secretary-General Antonio Guterres met with Yemen's foreign minister at UN headquarters amid warnings that an attack on Al Hodeidah was imminent.
More than 10,000 Yemenis have been killed since the war began, tens of thousands have been wounded, and another two million people have been displaced.
Saudi Arabia, the UAE and other Arab joined the Yemen war in March 2015, to help support the Yemeni government which had fled the capital Sanaa in 2014. It has damaged Yemen's infrastructure, crippled its health system and pushed the Arab world's poorest country to the brink of starvation.