Yemeni President Abdrabuh Mansur Hadi urged Shiite rebel leader Abdulmalik al-Huthi on Tuesday to withdraw his militant followers from the capital following the failure of negotiations on their demands.
In a letter to the rebel chief, of which AFP has obtained a copy, Hadi also called on the rebels to "complete their exit from Amran province" just north of Sanaa, after temporarily taking control in July.
The president also wants "a ceasefire in (neighbouring) Al-Jawf province" where pro-rebel tribes have been battling the army.
Hadi's letter sets out those conditions for a resumption of talks with the Zaidi Shiite rebels after the president's envoys last week came away without an agreement following three days of discussions with Huthi in Saada province, the rebels' northern stronghold.
Huthi's followers want the resignation of the government, seen as corrupt, the cancellation of a recent fuel price rise and a broader political partnership.
To support their claims the rebels mobilised armed fighters who have been camped out around Sanaa for the past week, while civilian activists have staged a sit-in near the interior ministry in the city centre.
Hadi, in his letter, asks the rebel chief to "remove the causes of the tension" to encourage a resumption of negotiations on the basis of "points agreed with the presidential delegation."
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He gave no details of the "points agreed".
The president requested Huthi to "appoint representatives to resume dialogue with the presidential delegation" in a last bid to ease the crisis in Yemen, where a wave of violence attributed to Al-Qaeda and a separatist movement in the south have accentuated economic problems.
UN special envoy to Yemen Jamal Benomar said the situation is "very worrying" and warned all sides that "a way out of the crisis is through concerted and peaceful effort".
Benomar, who is scheduled to present a report on Yemen to the UN Security Council on Friday, called on Yemenis to "hold back from any resort to violence for political ends" and "stop religious and regional campaigns of provocation".
The envoy added: "It is time for the state to exercise its authority over the whole of the country... as agreed in the conference of national dialogue," whose proposals included the principle of a federal state.
The impoverished country has been locked in a protracted transition since long-time strongman Ali Abdullah Saleh was forced from power in February 2012 after a deadly 11-month uprising.
Plans for a six-region federation have been rejected by both the Huthis and the southern separatists.