Ismail Ould Cheikh Ahmed, the United Nations special envoy to Yemen, left Houthi-controlled capital Sanaa on Monday, after a four-day official visit, to discuss a new UN-sponsored peace road map.

"I received positive response from the Houthi group and their ally of former President, Ali Abdullah Saleh's party," Ould Cheikh told reporters, upon his departure.

"I called on all Yemeni parties to engage in the peace road map. Political settlement is the only solution to end the war," he said.

Ould Cheikh gave no further details or outlined the road map.

But official sources in Houthi group had said that, the proposal would sideline internationally recognised President, Abd-Rabbu Mansour Hadi, dismiss Hadi's deputy, Ali Mohsen al-Ahmar, and transfer power to a new consensual vice president, and forming a new national unity government, which broadly includes Houthis and Saleh's loyalists.

Saleh welcomed the new UN proposal as "a good basis for negotiations," in a post on his official twitter.

The UN move came, after previous peace-mediated efforts to end the 19-month war between dominant Houthis, backed by Saleh's loyal forces, and Hadi's government army, backed by Saudi-led military coalition.

Ould Cheikh said, he will head to Riyadh, the Saudi capital, to meet Hadi and offer him the proposed road map.

However, Hadi chaired a meeting with his exiled cabinet in Riyadh a day earlier, criticising the UN envoy's proposal as "legitimising the Houthi and Saleh coup, and ignoring the UN Security Council (UNSC) Resolution 2216."

"The proposal would pave the way for more years of civil war and rewarding Houthis and Saleh the power," Hadi told the cabinet.

Hadi's administration also organised popular protests in government-controlled southern port city of Aden, to refuse the new UN envoy's road map and demand Hadi to stay as the legitimate president.

Yet, no official declaration was forthcoming, about the content of the new political settlement road map.

The UNSC Resolution, issued in 2015, demands that the Houthis withdraw from all areas seized during the latest conflict, relinquish arms seized from military and security institutions, cease all actions falling exclusively within the authority of the legitimate Yemeni government and fully implement previous council resolutions.

The war, since Saudi Arabia launched in Mar, 2015, air campaign in support of Hadi, against Iranian-allied Houthis, has killed over 10,000 Yemenis, mostly civilians and displaced three million others.