He is working with the parties on the details of the redeployments of forces, provision of security in the city and the opening of humanitarian access routes agreed in Stockholm, said Griffiths.
"I am pleased to report that both sides have largely adhered to the cease-fire in Hodeidah governorate that entered into force on Dec. 18, and there has been a significant decrease in hostilities since then," Griffiths told the Security Council.
The parties need to exert restraint in their media rhetoric, he said.
Apart from the Hodeidah cease-fire, the parties also agreed on a mechanism for prisoner exchange and reached an understanding on the city of Taiz, another frontline city.
"As agreed in Stockholm, we plan to hold a meeting of the Supervisory Committee to follow up on the prisoner exchanges on Monday, Jan. 14 in Amman. I hope these talks will allow many thousands of prisoners to go home and be reunited with their families."
The UN envoy commended the commitment and patience of the warring parties after the Stockholm consultations in mid-December. "Progress on implementation has been gradual and tentative, but it has made a tangible contribution to peace. There are doubtless many hurdles to be overcome in the days, weeks and months ahead, but the parties must not be diverted from their commitments."
UNITED NATIONS, Jan. 9 (Xinhua) -- The Yemeni government and Houthi rebels have largely honored their commitments to the Hodeidah cease-fire, said Martin Griffiths, the United Nations special envoy to Yemen, on Wednesday.
"I have talked with the parties and many prominent Taizis, and they all want the city to return to calm and for the people to have hope that the city will flourish once again. I am very happy that the Stockholm consultations provided a platform for them to agree to start working on this. I must therefore welcome the steps taken by the parties toward the creation of the mechanisms agreed in Stockholm, including the nomination of members of a joint committee."
Regarding Taiz, Griffiths said the parties agreed in Stockholm on the creation of mechanisms to reach consensus on how to address the situation there. Taiz is of enormous historic significance for Yemen as a whole and the city and its people have been a driving force in Yemen's economic and cultural life for many years, he said.
There has been some violence, including in Hodeidah city, and in the southern districts of the governorate. However, the violence is very limited compared with the scale before the Stockholm Agreement, he said.
The parties had agreed on a second round of talks for January 2019.
On the agreement for prisoner swap, Griffiths said the United Nations is working with both parties to finalize the lists of prisoners submitted by each party in Stockholm.
Griffiths was briefing the Security Council on the implementation of the commitments made by the parties in Stockholm in December 2018, which were collectively known as the Stockholm Agreement.
Gen. Cammaert has already chaired several meetings of the Redeployment Coordination Committee, with participation from representatives of both parties, to oversee the implementation of the Hodeidah cease-fire agreement.
"I am under no illusion that these are very sensitive and challenging days for both parties and for Yemen as a whole. The war goes on in other parts of the country. Which is why we need to make progress quickly."
"This will build the confidence of the parties, the Yemeni people and the international community in the implementation of the agreement and will lay the groundwork for further progress in the next round of consultations," he said.
Thanks to the swift authorization of the Stockholm Agreement by the Security Council through Resolution 2451, the United Nations has deployed an advance monitoring team to Hodeidah under the leadership of Patrick Cammaert of the Netherlands, he said. "This rapid deployment has given a clear signal to the parties and the Yemeni people of the international community's desire to turn the agreement into facts on the ground."
"This relative calm, I believe, indicates the tangible benefit of the Stockholm Agreement for the Yemeni people and the continued commitment of the parties to making the agreement work," said Griffiths via a video link from Amman, Jordan.
The next step is for the joint committee to meet and agree on a peaceful way forward for the city and its people, he said.
He indicated that the United Nations may not need to hurry into another round of talks. "We need to convene the next round but we need substantive progress on what was agreed in Stockholm. Otherwise the next round will only be a forum to discuss achievements of round 1. I heard this from both parties."
The file photo shows that Huthi female supporters demonstrate to support Huthi militias fighting Saudi-backed Yemeni government forces in the port city of Hodeidah, during a rally in the capital Sanaa, Yemen on Nov. 10, 2018. (AFP Photo)
"The activation of the Redeployment Coordination Committee is very welcome, and I urge both parties to continue to engage regularly and in good faith with Gen. Cammaert and his team so that the security arrangements and improvements in humanitarian access can be implemented swiftly, in line with what was agreed in Stockholm," he said.