Iranian Foreign Minister Mohammad Javad Zarif told Ban in a letter that Tehran stands ready to help the United Nations restore peace to Yemen, where the rebels have taken over the capital and driven President Abedrabbo Mansour Hadi into exile.
Hadi and Gulf allies accuse Iran of arming the Huthis, which Tehran strongly denies.
The four-point plan calls for a ceasefire and immediate end to all foreign military attacks, the urgent delivery of humanitarian and medical aid, a resumption of political talks and the formation of a national unity government.
The foreign minister added that "the only way to restore peace and stability is to allow all Yemeni parties to establish, without any foreign interference, their own inclusive national unity government."
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Zarif spoke with Ban by phone on Thursday, a UN spokeswoman said.
The Saudi-led coalition pounded Yemen yesterday as the air war entered its fourth week with little sign that the sides were ready to return to peace talks.
Ban has called for an immediate ceasefire, saying the country was "in flames" and all sides must return to political negotiations.
Saudi Arabia and its neighbors accuse Benomar of being duped by the Shiite Huthis who took part in peace negotiations as they pushed their offensive.
In his letter, Zarif said the situation in Yemen was "extremely alarming" and that the military intervention had destroyed hospitals, schools, food factories and other civilian infrastructure.
"This critical situation is escalating and humanitarian crisis in Yemen is approaching catastrophic dimensions," he added.