A Saudi-led military coalition allied with the Yemeni government against the Iran-backed Huthis announced it would allow for the evacuation of wounded rebels on a United Nations chartered plane Monday.
Speaking in Geneva, Lowcock said he is not expecting "easy or rapid process" in the peace talks being hosted by Sweden.
The UN envoy for Yemen Martin Griffiths said the coming days were a milestone and urged the parties not to "waver... let us work in good faith ... to deliver a message of peace".
Kuwait's Deputy Foreign Minister Khaled al-Jarallah told reporters that a Houthi delegation was now set to leave Sanaa for Stockholm on Tuesday morning together with his country's ambassador to Yemen.
Although no date has been announced for the start of the talks, Yemeni government sources say they could get under way on Thursday.
The first Yemen talks since 2016 are widely seen as the best chance yet for peace, as the worldwide community throws its weight behind efforts to resolve a conflict.
"We hope now that the UN-led consultations can begin later this week", Sweden's deputy UN Ambassador Carl Skau told reporters in NY.
"This is one step in the right direction towards the building of mutual trust among Yemeni communities", spokesperson Mirella Hodeib told AFP.
The extent of any Iranian support for the Huthis remains unclear, with some analysts saying its backing for the rebels was ramped up after the Saudi-led coalition began its campaign.
Yemen's government has said it has agreed to a large-scale prisoner swap with its adversaries, the Houthi rebels, as part of a "confidence-building measure", suggesting the warring sides could come to a ceasefire agreement at peace talks in Sweden later this week.
Yemeni government official Hadi Haig said between 1,500 and 2,000 members of pro-government forces and between 1,000 and 1,500 rebels would be released in the prisoner swap.
More than 10,000 people have been killed since the Saudi-led coalition joined the Yemen war in an attempt to bolster President Abedrabbo Mansour Hadi's standing against the rebels, who had seized the capital and a string of ports in a takeover the year before.
Rebel official Abdel Kader al-Murtadha confirmed the deal, adding that he hoped it would be "implemented without problem".
They agree that the future of the talks depends on two things: Riyadh's realisation that the world will no longer tolerate an open-ended humanitarian disaster in Yemen, and Tehran understanding that worldwide pressure on Riyadh to end the war will stop short of pushing Saudi Arabia to accept a strong Iranian influence in Yemen.
The executive director of the U.N.'s World Food Program, David Beasley, said Tuesday that 12 million people suffer from "severe hunger".
"This is not a country on the brink of catastrophe".
Residents in the port of Hodeidah, now a focus of the war, were fearful of renewed fighting if the talks failed as each side fortified their positions in the Houthi-held Red Sea city after a period of reduced hostilities.
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