Forces loyal to President Abedrabbo Mansour Hadi's government have been locked since 2014 in deadly battles with Iran-backed Shiite Huthi rebels who overran Sanaa late that year.
The conflict escalated in March 2015 when Saudi Arabia launched a military campaign to push back the rebels.
The war has left nearly 7,000 people dead, mostly civilians, according to the United Nations which had been struggling to convince the warring parties to implement a ceasefire and revive a stalled political process.
The contents of the roadmap which the envoy already presented to the rebels on Tuesday have not been made public.
But informed sources say it calls for agreement on naming a new vice president after the rebels withdraw from Sanaa and other cities and hand over heavy weapons to a third party.
Hadi would then transfer power to the vice president who would appoint a new prime minister to form a government in which the north and south of Yemen would have equal representation.
It cited Hadi as saying the plan "rewards the putschists while punishing the Yemeni people and legitimacy".
It was unclear how Hadi's Arab backers would react to his refusal, especially after a key coalition member, the United Arab Emirates, hailed the proposal on Thursday as a "political solution for the Yemeni crisis".
In August, US Secretary of State John Kerry outlined a similar plan which offered the Huthi rebels participation in government in exchange for an end to violence and a surrender of weapons to a third party.
But Saudi Arabia has not commented on the UN envoy's latest proposal and the rebels have yet to respond.
Warring parties in Yemen are under mounting international pressure to end the conflict that has left the already-impoverished country grappling with increasing cases of malnutrition and a spread of disease.
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