The pullback from Hudaida was initially agreed in December during talks in Sweden but deadlines for both sides to move their forces away from the ports and parts of the city were missed.
A preliminary compromise has been agreed between Yemen's warring parties to implement the Hudaida peace deal, the United Nations said in a statement on Thursday.
The compromise was agreed "pending further consultation by the parties with their respective leaders," the UN said.
The two sides have "given their commitment to respect the Hudaida ceasefire," but "are yet to agree to a preliminary agreement," it said.
Yemen's government and Houthi rebels agreed during talks in Sweden in December to a ceasefire in Hudaida, a redeployment of forces and access to humanitarian aid, under a deal seen as a major step towards ending the devastating war.
UN wants Houthis to stop blocking food storage
Earlier today, the UN aid chief urged Yemen's Houthi rebels to grant access in the coming days to a food storage site in Hudaida containing enough grain to feed millions of starving civilians.
The Houthis are refusing to allow UN aid agencies to cross front lines and reach the Red Sea Mills, which are located in a government-controlled area, because of security concerns, UN aid chief Mark Lowcock said.
"Access to the mills grows ever more urgent as time passes and the risk of spoilage to the remaining grain increases," said Lowcock in a statement.
"I implore all parties, in particular Ansar Allah affiliated groups, to finalize an agreement and facilitate access to the mills in the coming days."
Ansar Allah is the official name of the Shia Houthi movement, which controls Sanaa, much of Hudaida and other parts of Yemen in a war against the Saudi-backed Yemeni government.
The Red Sea Mills silos are believed to contain enough grain to feed 3.7 million people for a month but the granary has remained off-limits to aid organisations for more than four months.
The latest negotiations on securing access to the warehouses have dragged on and Lowcock deplored that a solution remained "elusive."
Hudaida port is the entry point for the bulk of Yemen's imported goods and humanitarian aid, providing a lifeline to millions in the Arab world's poorest country.
The United Nations has described Yemen as the world's worst humanitarian emergency, with 10 million people on the brink of famine.
Last month, two silos at the Red Sea Mills were hit by mortar shells, sparking a fire that destroyed some of the grain – probably enough to feed hundreds of thousands of people for a month, the United Nations said.