UNITED NATIONS -- UN Secretary-General Antonio Guterres expects the implementation of the first phase of Hodeidah troop withdrawal "will be carried out immediately" by the Yemeni warring parties, a UN spokesman said on Monday.

"There's always the need to have real impetus to implementation on the ground, and we hope that now that we have the first phase agreed, it will be carried out immediately, and we are expecting that will happen on the ground," Farhan Haq, deputy spokesman for the UN chief, told reporters at a regular briefing.

A deal reached in Stockholm in December 2018 says the Yemeni government and Houthi rebels should withdraw troops from the city of Hodeidah and ports of Hodeidah, Salif and Ras Issa. In a step forward, the two sides agreed on the first phase of the troop redeployment after holding talks on Saturday and Sunday.

On phase one, the agreement stipulates "they (opposing forces) needed to move out from the key ports, which is to say Hodeidah, Saleef and Ras Isa, and also from critical infrastructure such as the Red Sea Mills," Haq said.

Hodeidah is the major Red Sea port in Yemen, which handles some 70 percent of the food and fuel imports into Yemen.

The Red Sea mills currently store enough grains to feed 3.7 million people for a month, which is at risk of rotting, the UN's World Food Program has said.

A shaky cease-fire, as part of the Stockholm deal, has been in place in the region since December, but the Red Sea mills remain inaccessible to humanitarian workers.

Demilitarizing of the region is aimed at allowing humanitarian aid to reach Yemenis under the threat of famine because of the civil war now in its fourth year.

The Yemeni parties also agreed in principle on Phase 2 of the mutual redeployment. The next meeting on troop withdrawal is expected to convene within a week with the aim to finalize an agreement on phase two.