He also welcomed the expression of further openness toward the implementation of the prisoner exchange agreement between the Houthi rebels and the Yemeni government, and the desire for a political solution to end the conflict, said UN Secretary-General Antonio Guterres' press office in a "note to correspondents", Xinhua reported.
Griffiths stressed the importance of taking advantage of this opportunity and moving forward with all necessary steps to reduce violence, military escalation and unhelpful rhetoric, said the note.
"The implementation of this initiative by Ansar Allah in good faith could send a powerful message of the will to end the war," said the note, using the formal name of the Houthi rebels.
The special envoy reiterated his call on all parties to respect international humanitarian law, exercise restraint, and to spare Yemen from being drawn further into regional tensions, it said.
In a briefing to the Security Council on Monday, Griffiths warned that an attack on Saudi oil facilities may drag Yemen into "a regional conflagration."
The Houthis claimed responsibility for the September 14 attack, but Washington claimed that the attack was carried out by Iran.
Saudi Arabia has been leading an Arab military coalition against Iran-allied Houthis in Yemen for more than four years in support of the exiled internationally recognized government.
Griffiths has been shuttling between Sanaa and Riyadh to try to rescue a peace deal reached in Sweden in December 2018 between the Houthis and the Saudi-backed exiled government, including the prisoner exchange agreement.
( With inputs from IANS )