Updated

The U.N. envoy for Yemen said Thursday he fears "severe" humanitarian and political fallout if fighting intensifies in the crucial port city of Hodeida, but he's confident a pact can be forged to prevent increased violence.

Special Envoy Martin Griffiths has been trying to broker a cease-fire after a Saudi-led coalition launched an offensive last week to try to retake rebel-held Hodeida. The coalition is allied with Yemen's internationally recognized, exiled government.

"I am confident that we can reach an agreement to avert any escalation of violence" in Hodeida, Griffiths said in a statement Thursday, noting that he feared any military escalation "would have severe political and humanitarian consequences."

He said he was encouraged by meetings in recent days with leaders of the Shiite rebels, known as Houthis, and plans to meet with government leaders.

Hodeida is the main entry point for food, humanitarian aid and fuel supplies to impoverished Yemen, already on the brink of famine after three years of war. It began after the Iranian-backed Houthis and their allies seized Yemen's capital, Sanaa, in September 2014.

The war has killed over 10,000 people and thrust the Arab world's poorest country into what the U.N. has called the world's worst humanitarian crisis. Around two-thirds of Yemen's population of 27 million relies on aid, and over 8 million are at risk of starving.

Aid groups have expressed alarm about the Hodeida offensive, fearing a protracted fight could shut down the port and potentially tip millions of people into starvation.

Seeking to allay concerns, diplomats from Saudi Arabia and the United Arab Emirates outlined a roster of humanitarian activities and plans Thursday at a New York news conference. The UAE has played a leading role in the coalition operation in Hodeida.

"The coalition has made humanitarian relief a priority," the Emirati U.N. Ambassador Lana Nusseibeh said as she and Saudi officials said their countries were providing tons of food, trucks and aircraft to transport humanitarian supplies, and other help. The two nations also together gave more than $900 million to U.N. humanitarian efforts in Yemen earlier this year.

The coalition has previously faced criticism for a campaign of airstrikes that has killed civilians and destroyed hospitals and markets.

The Houthis, meanwhile, have laid land mines, killing and wounding civilians. They have also targeted religious minorities and imprisoned opponents.

Rebel leader Abdel-Malek al-Houthi vowed in a speech Wednesday to continue the fight.