Martin Griffiths told the Security Council by video link from Amman that "when — and I hope it is when and not if — these redeployments happen they will be the first voluntary withdrawals of forces in this long conflict."
He said agreement on the first phase of withdrawals was reached in negotiations between the parties and Lt. Gen. Michael Lollesgaard, who heads the UN operation monitoring a broader cease-fire and redeployment agreement reached in Sweden in December. The Sweden agreement has been marred be repeated violations and delays.
Griffiths called Hodeida, whose port handles about 70 percent of Yemen's commercial and humanitarian imports, "a test of many things," including leadership, and he expressed hope "that we shall see in the coming days the people's trust vindicated in this."
The conflict in Yemen began with the 2014 takeover of the capital, Sanaa, by the Iranian-backed Houthis. A Saudi-led coalition allied with the internationally-recognized government has been fighting the Houthis since 2015.
The fighting in the Arab world's poorest country has killed thousands of civilians, left millions suffering from food and medical care shortages, and pushed the country to the brink of famine.
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There have been lengthy delays in implementing the Sweden agreement, which the UN and diplomats blame largely on the lack of trust. There has been concerted international pressure to implement the Hodeida deal, which is widely seen as a crucial first step toward much more difficult negotiations to end the war.
A UN official has said the first phase of redeployment involves a pullback of several kilometers (miles) by the Houthis and coalition forces, and the second phase involves a withdrawal of 18 to 30 kilometers (11 to18 1/2 miles), depending on the location and fighters. In some places in Hodeida city, the opposing forces are facing each other about 100 meters (yards) apart, the official said.
Griffiths told the Security Council he was grateful to President Abed Rabbo Mansour Hadi, who has repeatedly told him he wants "to see these redeployments happen," and to Houthi leader Abdul Malik at Houthi, who reconfirmed his support for the Hodeida agreement when they met in the capital, Sanaa, last week.
"We will now move with all speed towards resolving the final outstanding issues related to phase two and the status of local security forces," Griffiths said.
Nonetheless, he remained cautious.
Griffiths reminded the council that when he first briefed members almost a year ago he said "a political solution was available to resolve the conflict," but added "that at any time war can take the chance of peace off the table."
"Both these propositions hold true as much today as a year ago," Griffiths said.