UN Secretary-General Antonio Guterres has assured Yemen's leader that the world body will remain impartial in efforts to resolve the country's conflict, rejecting accusations that its envoy was siding with rebels.

The pledge came in a letter from Guterres to President Abedrabbo Mansour Hadi, who had accused the UN special envoy to Yemen of impartiality.

"I would like to assure you that every effort will be made to maintain the impartial stance that is expected of the United Nations," while implementing a ceasefire agreement, Guterres said in the letter seen by AFP on Sunday.

In his own letter addressed to Guterres, Hadi accused envoy Martin Griffiths of "providing the Huthi militia with guarantees to stay in Hodeida and its ports under the umbrella of the UN".

"I can no longer accept these offences by your special envoy which threaten chances to find a (lasting) solution," Hadi said.

Hodeida is the main entry point for the bulk of Yemen's imports and humanitarian aid, providing a lifeline to millions of people.

Earlier this month the United Nations supervised the rebels' handing over of the ports of Hodeida, Saleef and Ras Issa to a "coast guard", but the government said they were in fact Huthi forces in different uniforms.

The pullback is in line with a ceasefire deal for Hodeida reached in Stockholm in December.

Guterres said that he and Griffiths were prepared "to discuss the legitimate concerns of the government of Yemen referenced in your letter, which we take very seriously."

Government forces -- backed by a Saudi-led military coalition -- and the Iran-aligned Huthi rebels have been locked in a four-year war that has pushed the country to the brink of famine.

Tens of thousands of people, mostly civilians, have been killed.

The conflict has triggered what the UN describes as the world's worst humanitarian crisis with more than two-thirds of the population in need of aid.