The Houthi rebels said the peace initiative could be a lasting commitment if the Saudi-led coalition fighting in Yemen stopped air strikes and lifted port restrictions.
The Houthis have been attempting since February to capture oil-rich Marib to consolidate their control over the northern part of war-torn Yemen.
Return of Houthi prisoners to capital, Sanaa, comes two days after the Saudi-led military coalition announced freeing 200 Houthis, a decision the UN hailed.
Military coalition spokesman Turki al Maliki announces release of Houthi prisoners, says restrictions on air space will be eased to allow flights out of rebel-held airport in capital Sanaa.
It is the first air strike that the alliance has confirmed carrying out at the airport since peace talks last week in Sweden.
Delegates of Yemen's warring government and Houthi rebels say they have set January 20 as a final date to exchange prisoners from both sides, in a mass swap deal.
The ongoing war in Yemen has led to thousands of innocent civilians dying. The irony is that the people investigating the crimes, are the same people doing the bombing.
Russian Foreign Ministry spokeswoman Maria Zakharova said in a statement that the diplomats will fulfill their duties from the Saudi capital, Riyadh.
Officials at Sanaa airport said two other UN flights had arrived on Saturday.
United Nations welcomes Saudi Arabia's move to reopen Hodeida port and Sanaa airport for humanitarian aid.
More than 10,000 people have died due to their inability to travel for life-saving treatments. That’s because of a year-long blockade of the airport in the capital, according to Yemen’s health ministry.
Cholera is easily treatable, yet Yemeni authorities are struggling to fight a cholera epidemic that is spiralling out of control amid a brutal bombing campaign.
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