"We don't think that a resolution is needed at this time," Ambassador Abdallah al-Mouallimi told a news conference.
His remarks came after the 15-member council expressed grave concern for the worsening situation in Yemen, where the coalition launched air strikes nearly a year ago to back Yemeni forces fighting Shiite Hutu rebels.
The council is considering a new resolution to press for more humanitarian aid deliveries and to stress the importance of protecting hospitals from attacks.
The United Nations says more than 80 percent of the population is in dire need of food, medicine and other basic necessities and the crisis ranks as a "Level 3 emergency", the most serious in the UN system.
Mouallimi said that UN aid officials and the UN envoy for Yemen, Ismail Ould Cheikh Ahmed, agreed with him that there is no need for new action by the Security Council.
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Asked about the ambassador's comments, the UN office for the Coordination of Humanitarian Affairs said: "OCHA cannot comment on what a diplomat may say he has heard. The Security Council takes such decisions and makes such recommendations as it sees fit."
The ambassador cautioned that any new resolution could prolong the war "because the Huthis would now feel that they have a new lease on life with something other than 2216."
Adopted last year, Resolution 2216, which was drafted by Saudi Arabia and its Gulf partners, demands that the Huthis withdraw from all territory seized in their offensive.
More than 6,000 people have been killed in Yemen since the coalition began its air strikes campaign in late March last year.
The United Nations is pushing for peace talks between the Saudi-backed Yemeni government, the Huthi rebels and their allies, but those efforts have been deadlocked over disagreements on a ceasefire.
Mouallimi said he hoped that talks could resume by March 15.