The United Nations' special envoy to Yemen, Martin Griffiths, said on Tuesday he plans to present a peace plan within two months to end the conflict, but cautioned against military escalation.
Mr Griffiths, a former British diplomat who replaced Mauritania's Ould Cheikh Ahmed 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," Mr Griffiths said.
He warned, however, there were 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".
A Saudi-led military coalition intervened in the conflict in Yemen in 2015, backing the internationally-recognised government forces fighting Iran-allied Houthi rebels. Iran has denied supplying weapons to the Houthis.
"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 denied this, however, saying "we don't have the intention to advance on Hodeidah".
Coalition and Yemeni forces have made territorial gains in recent months against the Houthi rebels in an armed push moving northward from the Bab Al Mandab strait toward Hodeidah on the Red Sea, where 80 per cent of Yemen's crucial food imports arrive.
Houthis threatened, in January, to blockade the port city if coalition forces continued their push towards the Red Sea coast city.
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 — a claim Tehran denies.
US Ambassador to the UN 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," Ms Haley told the council.