The United Nations' Yemen mediator Martin Griffiths said on Tuesday he plans to present a plan for negotiations within two months to end the conflict, but warned that any new military offensives could "take peace off the table."
A proxy war is playing out in Yemen between Iran and Saudi Arabia.
A Saudi-led military coalition intervened in Yemen in 2015, backing government forces fighting Iran-allied Houthi rebels.
Iran has denied supplying weapons to the Houthis.
Griffiths, a former British diplomat who replaced Mauritania's Ould Cheikh Ahmed as the UN Special Envoy last month, briefed the UN Security Council for the first time on Tuesday.
"My plan is to put to the (Security) Council within the next two months a framework for negotiations," Griffiths said.
He warned, however, there were unconfirmed reports that movements of forces in Yemen are on the increase and the prospect of intense military operations around the Houthi-held port city of Hodeidah "may soon be forthcoming."
"Our concern is that any of these developments may in a stroke, take peace off the table," he said. "We all need urgently and creatively to find ways to diminish the chances of these game-changing events, upsetting and derailing the hopes of the great majority of Yemenis."
Yemen's UN Ambassador Khaled Hussein Mohamed Alyemany told reporters: "We don't have the intention to advance on Hodeidah."
Coalition and Yemeni forces have made modest territorial gains in recent months against the group in an armed push moving northward from the Bab al-Mandab strait toward Hodeidah on the Red Sea, where 80 percent of Yemen's crucial food imports arrive.
The war has killed more than 10,000 people, displaced more than 2 million and driven the country to the verge of famine.
The Houthis have repeatedly fired missiles at Saudi Arabia, which the United States and UN experts say were of Iranian origin. Tehran denies the charge.
US Ambassador to the United Nations Nikki Haley said on Tuesday she would continue to push the Security Council for accountability.
"To achieve enduring peace in Yemen, Iran must stop its interference and its violations of the arms embargo this Council imposed," Haley told the council.
The Saudi-led coalition has conducted thousands of air strikes targeting Houthi fighters and has often hit civilian areas, although it denies ever doing so intentionally.
"We have called on all parties to take appropriate measures to mitigate the risk of civilian casualties," Haley said. "The United States is working to offer support to the Saudi-led Coalition, while minimizing civilian casualties."