The peace talks are set to resume in Stockholm this week with delegations from the Iran-allied Houthis and the Yemeni government, backed by Saudi Arabia and the UAE, reportedly set to be in attendance.
Prospects for convening talks have risen as Western allies press Saudi Arabia, leader of the Sunni Muslim alliance battling the Iranian-aligned Houthis, over a war that has killed more than 10,000 people and pushed Yemen to the brink of starvation.
The coalition agreed to facilitate the medical evacuations at the request of United Nations envoy Martin Griffiths for "humanitarian reasons" and as a "confidence-building" measure, Maliki said in the statement early on Monday.
Yemen talks set to start in Sweden after wounded Houthis evacuated
The fate of wounded rebels had been a stumbling block to the start of a previous round of aborted peace talks in September.
Previously, a representative of the Ansar Allah Houthi organization told Sputnik that Houthis were ready to take part in talks on Yemen in Sweden, but demanded that the United Nations resolved the issue of providing the aircraft, issuing the permit for its departure and the delegation's security.
The murder of Saudi journalist Jamal Khashoggi has increased the pressure on the kingdom to end its military campaign in Yemen. Three-quarters of impoverished Yemen's population, or 22 million people, require aid.
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These include Sanaa and the port city of Hodeidah, now a focus of the war.
World Food Program chief David Beasley said in Geneva that an upcoming food security report would show an increase in severe hunger rates in Yemen - where a child dies every 11 minutes - but not necessarily meet the criteria of starvation. "A stable state, important for the region, can not coexist with unlawful militias".
"If the Yemeni capital's airport is not opened to the Yemeni people in the peace talks in Sweden, I call on the (Houthi) political council and government to close the airport for all planes", Mohammed Ali al-Houthi tweeted. "The focus of the talks on the future management of the Hodeidah port and city and de-escalation of the fighting are important and welcome", David Miliband, President and CEO of the International Rescue Committee, said in a statement.
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The Canadian government provides aid to Yemen, which faces the worst humanitarian crisis in the world.
Sources close to the rebels told AFP the Houthis are expected to request the reopening of Sanaa International Airport, which has been damaged by Saudi-led air raids and shut down by Riyadh and its allies, who control Yemen's airspace.
In Geneva, Lowcock said the Yemeni government would need billions of dollars of support to finance core state functions after oil revenues fell about 85 percent, leaving annual income at $2 billion.
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"Yemen needs an immediate cease-fire and concrete steps to restore public services", it said in a statement.