The announcement from the UN came as a Saudi-led coalition pressed its air war against the Iran-backed rebels into a fourth week, promising "no half measures" in its campaign to restore President Abedrabbo Mansour Hadi.
As UN envoy, Jamal Benomar had tried desperately to avert all-out conflict as the Shiite Huthi rebels seized the capital last September and then placed Hadi under effective house arrest in January.
But Hadi's escape to second city Aden the following month to rally opposition to the rebels effectively brought negotiations to an end and Benomar's efforts to revive them came to nothing as the rebels advanced on the president's last refuge, triggering his flight to Saudi Arabia.
Last month, a Gulf diplomatic official accused the UN envoy of appeasing the rebels and their allies as they overran Saudi Arabia's impoverished but strategically important neighbour.
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"They pressed to redraw the political map of Yemen and, in a way, they were encouraged by Benomar," the official said.
The Moroccan diplomat had been instrumental in negotiating a peace deal that eased former president Ali Abdullah Saleh out of office in February 2012 after a year of bloody protests against his three-decade rule, and Ban paid tribute to his work.
Among the candidates to replace him is Mauritanian diplomat Ismail Ould Cheikh Ahmed, who currently heads the UN Ebola mission in Accra, a UN official said, speaking on condition of anonymity.
Benomar's resignation came hot on the heels of the adoption by the UN Security Council of a resolution that the Saudi-led coalition saw as support for its bombing campaign.
The resolution -- the first formal action taken by the Security Council since air strikes started on March 26 -- demands that the rebels withdraw from Sanaa and all other areas they have seized.