RIYADH: The UN envoy to Yemen said on Thursday the redeployment of rival factions in the key port city of Hodeidah is "slow" but will happen. Martin Griffiths made the comments as Saudi Deputy Defense Minister Prince Khalid bin Salman discussed the Yemen cease-fire deal with US Secretary of State Mike Pompeo in Washington. Prince Khalid and Pompeo "agreed on the need for parties to adhere to the agreement made in Sweden," the US State Department said. Pompeo expressed his appreciation for Saudi Arabia’s continued support for Griffiths’ efforts "to advance the political process in Yemen." The deal between the Yemen government and Houthi militants was signed in the Swedish capital in December, and while leading to a reduction in hostilities in the city, it has since stalled. Griffiths told The Associated Press that the cease-fire in the key port held seized by the militants near the start of the conflict is holding. "As I"ve been reminded recently there are 50 percent fewer civilian casualties in Hodeidah since the cease-fire came into account than in the previous three months," Griffiths said. "So that"s quite a change and that"s good for the people of Hodeida, but we need to go further. We need to quickly see those redeployments happening." Griffiths said the two sides are meeting daily to finalize details of the first redeployment from the Hodeidah port and two smaller ports. That will be followed by a second phase in which heavy weapons and ground forces will be removed from the city, he said. Griffiths said if the first phase is successful, the ensuing demilitarization phase will be much easier. "Yes, it"s slow, we shouldn"t be surprised, but we need to keep the pressure up." Griffiths told the Security Council last month that he is "optimistic" the cease-fire will hold and the redeployments will take place. Hodeidah is the main entry point for aid to Yemen, where nearly four years of war has spawned the world"s worst humanitarian crisis. The war in Yemen started in 2014 when Houthi rebels swept the northern part of the country and forced the internationally recognized government to flee before seeking military intervention by an Arab coalition that inludes Saudi Arabia. Griffiths warned that the alternative to peace is "unthinkable" humanitarian disasters. "It is the possibility of famine, the increasing cholera that we are now seeing, and a massive humanitarian aid program which barely keeps pace with the growing needs of the Yemeni people," he said. "We can"t allow that to replace peace in Yemen." Yemen is the world"s worst humanitarian crisis, with nearly two thirds of its people in need of some sort of aid and 3 million displaced. Thousands have died of malnutrition, preventable diseases and epidemics.