Tim Lenderking, who has been pushing for a ceasefire between the Houthis and a Saudi-led military coalition, also told a virtual media briefing that all ports and airports in Yemen should be opened to ease a humanitarian crisis.
Riyadh had in March proposed a nationwide ceasefire and the reopening of air and sea links to bolster efforts to end a conflict widely seen as a proxy war between Saudi Arabia and Iran.
But the initiative has been stuck since the Houthis made a series of counter-proposals, including fully lifting the coalition's blockade before any truce deal.
Lenderking said the United States would on Thursday impose sanctions on the head of the general staff leading the Houthi offensive in Marib, Mohamad Abdulkarim al-Gamali, and on a prominent leader of Houthi forces assigned to the advance on Marib, Yousuf al-Madani.
"If there were no offensive, if there were commitment to peace, if the parties are all showing up to deal constructively with the U.N. envoy there would be no need for designations," he said.
The Houthi offensive in Marib was going nowhere and was only endangering more than 1 million people, he said, while stressing that all economic arteries, including ports and airports.
The envoy welcomed direct talks between Saudi Arabia and Iran as constructive but said he has not yet seen positive Iranian engagement towards ending the conflict in Yemen, which has killed tens of thousands of people and pushed millions to the brink of famine.He called on Tehran to support peace talks and said Washington wants a long-term solution that goes beyond a ceasefire, which the envoy said was the only way Yemenis would get the humanitarian relief they require.