The Houthis are said to be allied with Iran, though how much is in dispute.
"We have some 21 million people needing assistance and seven million of those are in famine-like conditions and rely completely on food aid", United Nations humanitarian coordinator for Yemen Jamie McGoldrick said.
Air traffic in Sanaa's airport is now restricted to flights carrying humanitarian aid sent by the United Nations and other global organizations.
The blockade "is complicating what is already a catastrophic situation", McGoldrick said.
While the language of the resolution calls to "increase efforts to adopt all necessary and appropriate measures to prevent civilian casualties and increase humanitarian access", it does not call for an end to US support of the Saudi-led coaltion attacking Yemen.
Tuesday's move to ease the blockade came three days after the coalition reopened Aden seaport and Alwadiah land border crossing between Saudi Arabia and northeast Yemen, but the coalition has kept the Houthi-controlled northern ports shut.
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Saudi Arabia announced it shut down all ports after a November 4 ballistic missile attack on Riyadh near its global airport by the Shiite rebels known as Houthis.
However, McGoldrick said earlier in the day that there was "no indication" the coalition was actually lifting the blockade in line with its announcement.
McGoldrick says access to such ports is "helpful" but that the key need is access to the rebel-held Red Sea ports of Salif and Hodeida, closer to large population centers.
Humanitarian agencies had been successful in preventing starvation and tackling a cholera outbreak that has sickened more than 900,000 people in six months and killed over 2,200. The officials spoke on condition of anonymity because they weren't authorized to speak to the media.
The Saudi-led coalition hopes that will prevent "the smuggling of weapons, ammunitions, missile parts and cash that are regularly being supplied by Iran and Iranian accomplices to the Houthi rebels", the statement said.