The evacuation of wounded and other civilians from the villages is a condition for the evacuation of people in the besieged rebel zone of Aleppo, Syrian state media reported on Sunday.
Late on Sunday, the United Nations Syria aid chief Jan Egeland said the first evacuations from the two villages would take place overnight, but added in a message on Twitter that thousands more waited to depart.
In the last rebel area of Aleppo, thousands are still waiting to leave, people there have said, many of them without homes after having been displaced during the fighting of recent weeks.
The Syrian army and its allies made swift advances from November 24 across east Aleppo, which rebels fighting to oust President Bashar al-Assad had held for years, under an intense bombardment.
Defeating the rebellion in Aleppo, which was Syria's largest city before the war, will constitute Assad's biggest victory in the civil war which began in 2011 with mass protests against his rule.