The United Nations will present a new plan for the pullback of forces from Yemen's flashpoint city of Hodeida following talks with the government and Houthi rebels, a UN envoy said Tuesday.

The redeployment of forces was agreed in December under a ceasefire deal reached in Sweden that offered the best hope in years of moving toward an end to the war that has pushed Yemen to the brink of famine.

"Following constructive discussions with both parties, there is significant progress towards an agreement to implement phase one of the redeployments of the Hodeida agreement," said a statement from Martin Griffiths, the UN envoy for Yemen.

"Operational details will be presented to the parties in the Redeployment Coordination Committee (RCC) for endorsement shortly," he added.

The UN envoy's statement did not give a date for the start of the pullback, which would mark the first step towards de-escalation.

Griffiths said he "looks forward to the swift endorsement of the plan."

The United Nations announced a deal on the two-stage pullback from Hodeida city and its ports on February 17, but the redeployment failed to materialize on the ground.

UN diplomats said the Huthis were refusing to pull away from the ports as part of the first stage, citing fears that forces linked to the Saudi-led coalition will move in to take over those facilities.

Griffiths and head of the RCC, Danish General Michael Lollesgaard, have been holding talks with all sides to overcome the final hurdles.

The Red Sea port of Hodeida is the entry point for the bulk of imported goods and relief aid to Yemen.

The Saudi-led campaign in Yemen will begin its fifth year on March 26, with millions of civilians facing famine.

The conflict has unleashed the world's worst humanitarian conflict.