The Houthis refused a UN proposal to withdraw from the city of Hodeidah and its port and to hand over management to the UN, Al Arabiya English's correspondent in New York reported.
The Houthis have instead proposed that Hodeidah and its port be under joint management with the UN.
These developments were conveyed to the UN Security Council during a closed-door briefing by UN Special Envoy for Yemen Martin Griffiths who informed the council of the results of his talks in Sanaa and Aden.
Meanwhile the Security Council gave strong backing to efforts by Griffiths to start new talks between Yemen's warring parties and reaffirmed that "a political solution remains the only way to end the conflict."
Council members said they "encouraged all parties to engage constructively with his efforts to take forward a political solution."
The Security Council reiterated its call for Hodeidah and the port of Saleef "to be kept open and operating safely given the continuing risk to the grave humanitarian situation."
Previous peace efforts have failed but Griffiths, who was appointed to the post in February, expressed optimism in a statement Wednesday after meeting top Houthi leaders in Sanaa.
Griffiths said without elaborating that the rebels and their allies have expressed a "strong desire for peace" and discussed "concrete ideas for achieving peace." But a Houthi negotiator said there was no breakthrough in negotiations.
Griffiths had in the past three days held “fruitful” talks in Sanaa, as he described them, where he was trying to convince Houthi leaders, including Abdulmalik al-Houthi, to hand over Hodeidah and its port and to prepare the atmosphere for resuming consultations towards reaching a political solution according to a plan he will present in the next weeks.
Well-informed sources in Sanaa said so-called Supreme Political Council Mahdi al-Mashat asked the UN envoy for some time to respond to his plan that aims to avoid further escalation in Hodeidah.
The sources, however, added that Houthi leaders are only trying to buy time as they continue to send more reinforcements towards Hodeidah.