The Arab alliance intervened in the war in 2015 to restore the internationally recognised government of Abd-Rabbu Mansour Hadi but has bogged down in military stalemate, despite superior air power, since seizing the southern port of Aden that year.
"Evacuating wounded Houthi fighters from Sanaa once again demonstrates the Yemeni government & the Arab coalition's support for peace", Gargash said in a tweet.
The UN food agency said it was planning to scale up food distribution rapidly to help another four million people in Yemen over the next two months, more than a 50 per cent rise on the number now reached.
Michael Aron, the British ambassador to Yemen, said he will participate in the talks alongside 23 other ambassadors and Griffiths, the United Nations envoy.
Griffiths was in Sanaa earlier this week to meet with Houthi rebel leaders, and he then travelled to Sweden with a Houthi delegation on Tuesday.
Saudi Arabia is unlikely to tolerate what it views as an Iranian proxy on its doorstep, and the Houthis have little incentive to withdraw from the capital and other territories they have captured and held at great cost.
The fate of wounded rebels had been a stumbling block to the start of a previous round of aborted peace talks in September.
The government said the Houthis had persistently used the port as a way to raise income and to smuggle in arms.
The UN envoy arrived in Sana'a on Monday in a bid to pave the way for peace talks, which come after almost four years of war that have led to displacement, food insecurity, outbreaks of cholera and diphtheria across the country.
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The deal was struck by Griffiths, who was in the rebel-held capital Sanaa for meetings already buoyed by the evacuation of the wounded insurgents - a key rebel precondition for the talks.
In the words of one: "The Iranians possibly feel that this is the time to move forward because they can see that pressure is being applied by the West on Riyadh to act promptly to bring an end to the war which is why they made a decision to support the talks".
Yemeni government representatives were expected to join a rebel delegation in Sweden for high-stakes peace talks.
The conflict, seen as a proxy war between Riyadh and Tehran, has left over 8 million Yemenis facing starvation although the United Nations has warned this could rise to 14 million.
Intensified fighting around Yemen's port city of Hodeida has cut port operations by almost half.
"A stable state, important for the region, can not coexist with unlawful militias", Gargash said.
Griffiths hopes to reach a deal on reopening Sanaa airport and securing a prisoner swap and a ceasefire in Hodeidah as a foundation for a wider truce, including a halt to coalition air strikes that have killed thousands of civilians and Houthi missile attacks on Saudi cities.
"Tehran is ready to help worldwide talks to end the crisis and underlines the importance of accelerating providing humanitarian aid to the people", Iran's foreign ministry said in a statement, according to Reuters.