"We demand, after a complete end to the aggression against Yemen and the lifting of the blockade, to resume political dialogue... under the sponsorship of the United Nations," Mohammed Abdulsalam, the spokesman for the Huthi rebels, said in a statement.
Saudi-led warplanes launched new strikes Wednesday on rebel positions in Yemen's third city Taez after the coalition had warned it stood ready to counter any advance by the rebels and their allies.
Read: Pakistan welcomes end of Saudi-led military coalition in Yemen
The Houthi rebels' spokesman praised the United Nations' "positive efforts and its declared support for national dialogue".
His remarks came despite the UN Security Council's adoption last week of a resolution that slapped sanctions on the rebels and demanded they immediately withdraw from territory seized.
The UN had sponsored a Gulf-brokered peace deal that eased former president Ali Abdullah Saleh out of office in February 2012, ending a year of nationwide bloody protests against his three decades of iron-fisted rule.
Read: Decisive Storm: Saudi-led coalition calls off Yemen operation
But the UN envoy to Yemen, Jamal Benomar, resigned last week after he lost Gulf countries' support, according to diplomats.
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