The move marks a major reversal by the rebels, who previously dismissed the government's insistence on their withdrawal from Afar and Amhara for talks to begin as "an absolute non-starter".
Rebellious Tigrayan forces fighting the central government are withdrawing from neighbouring regions in northern Ethiopia, a step towards a possible ceasefire after 13 months of brutal war.
"We trust that our bold act of withdrawal will be a decisive opening for peace," wrote Debretsion Gebremichael on Monday, the head of the Tigray People's Liberation Front (TPLF).
His letter to the United Nations called for a no-fly zone for hostile aircraft over Tigray, imposing arms embargos on Ethiopia and its ally Eritrea, and a UN mechanism to verify that external armed forces had withdrawn from Tigray.
Ethiopian government spokesperson Legesse Tulu did not immediately respond to a request for comment.
Debretsion said he hoped the Tigrayan withdrawal, from the regions of Afar and Amhara, would force the international community to ensure that food aid could enter Tigray.
The United Nations has previously accused the government of operating a de facto blockade – a charge the government has denied.
"We hope that by (us) withdrawing, the international community will do something about the situation in Tigray as they can no longer use as an excuse that our forces are invading Amhara and Afar," TPLF spokesman Getachew Reda told Reuters news agency.
Other proposals in the letter include the release of political prisoners – thousands of Tigrayans have been detained by the government – and the use of international investigators to pursue those responsible for war crimes.
Last week the United Nations agreed to set up an independent investigation into rights abuses in Ethiopia - a move strongly opposed by the Ethiopian government.
International mediators including the African Union and United States have repeatedly tried to negotiate a ceasefire between the two sides to allow aid to enter Tigray but both sides refused until certain conditions were met.
The conflict erupted last year between the federal government and the TPLF, which dominated Ethiopian politics for nearly three decades before Prime Minister Abiy Ahmed came to power in 2018.
In June, the military withdrew from Tigray after reports of mass killings of civilians, gang rapes and blocking of aid supplies.
The government has said it has prosecuted individual soldiers although it has provided no details.
In July, Tigrayan forces invaded Afar and Amhara.
The Ethiopian military launched an offensive at the end of November that pushed the Tigrayan forces back hundreds of kilometres.
Thousands of civilians have been killed in the war, around 400,000 are facing famine in Tigray, and 9.4 million people need food aid across northern Ethiopia as a result of the conflict.