The first redeployment of forces in Yemen's flashpoint city of Hodeida could possibly begin later on Tuesday or the following day, a United Nations envoy said, marking the first concrete step toward de-escalation in the war.

Yemen's government and Houthi rebels agreed on Sunday to the first phase of the pullback of forces, which is a key provision of a ceasefire deal reached in December in Sweden.

UN envoy Martin Griffiths told the Security Council that the sides had agreed to pull back from the rebel-held ports of Saleef and Ras Issa followed by a redeployment from Hodeida port, also held by the Houthis, and critical parts of the city.

"With the beginning, possibly even today or tomorrow, of the implementation of that part of the Hodeida agreement, we now have the opportunity to move from the promise made in Sweden to hope now for Yemen," Griffiths told the council, speaking by video conference from Amman.

The pullback would also allow access in the coming days to the Red Sea Mills food warehouses, which are believed to contain enough grain to feed 2.7 million for a month, UN aid chief Mark Lowcock said.

The fragile Stockholm ceasefire deal for Hodeida marks the first step toward ending a devastating war that has pushed Yemen to the brink of famine.

The Red Sea port is the entry point for the bulk of imported goods and relief aid to Yemen, which the United Nations has described as the world's worst humanitarian crisis.

Yemen's rebels have been locked in a war with government forces backed since 2015 by a Saudi-led coalition.