The envoy, Ismail Ould Cheikh Ahmed, was to "try to present (Hadi) the latest peace proposals" to end the nearly two-year war, said UN spokesman Farhan Haq.
The United Nations said the civilian death toll in fighting since a Saudi-led force intervened in March 2015 had reached 10,000, up from the previous figure of 7,000.
The higher toll "underscores the need to resolve the situation in Yemen without any further delay", said Haq.
Ould Cheikh Ahmed is hoping to revive peace prospects in Yemen after Hadi rejected his proposed roadmap. He is due to report to the UN Security Council later this month.
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The roadmap provides for a new unity government in Yemen and a rebel withdrawal from the capital and other cities.
Under the proposal, Hadi's powers would be dramatically diminished in favour of a new vice president who would oversee the formation of the interim government that will lead a transition to elections.
The envoy has been holding talks in the Gulf in recent weeks, including in Riyadh, where he met with Yemen's central bank governor to ease a cash crisis in rebel-held areas.
The United Nations ranks the conflict in Yemen as one of the world's worst humanitarian crises.
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