Speaking at a Security Council meeting on Friday, Grundberg said that civilians, including women and children, were bearing the "brunt of escalating violence." He warned that regional instability was both driving and being driven by events in Yemen.
"Ongoing instability in the Middle East continues to impact dynamics in Yemen, while developments in Yemen, in turn, reverberate across the region," he said.
The envoy stressed that "unless war is to become Yemen's permanent reality, the time to consider political strategies is now." He added that "gains on the battlefield cannot substitute for the negotiations that will be required to settle the conflict" and urged Security Council members to support mediation efforts.
According to the UN, at least 46 civilians have been killed and more than 130 injured since August, with children disproportionately affected.
Yemen's UN representative for the internationally recognised government, Abdullah Ali Fadhel al-Saadi, told the council that the Houthi threat was no longer an "internal Yemeni affair" and called for "decisive, practical measures" to cut the flow of funding, weapons and technology to the group, which is backed by Iran.
The warning comes as Houthi attacks on Saudi Arabia continue. Saudi authorities reported on Friday that King Khalid International Airport north of Riyadh was attacked twice on Thursday, killing three Saudi citizens. Saudi envoy Abdulaziz al-Wasil called on the council to address the "dangerous escalation" by the "terrorist Houthi militias," stating that Riyadh would "not allow Yemen to be turned" into a launch pad for attacks.