Russia, which helped to broker the deal with Turkey, said its operation was now "complete" with all women and children moved from the city.
Ankara and a Syrian military source said the evacuation had been suspended but was not yet over.
"The evacuations are not over and many people still want to leave the area," said Turkish Foreign Minister Mevlut Cavusoglu.
Amid the confusion, a convoy of evacuees that had already left the east when the operation was suspended was forced to return to rebel territory, an AFP correspondent said.
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But on Friday morning it was abruptly suspended, with the government accusing rebels of violating the terms of the accord.
"The evacuation operation has been suspended because the militants failed to respect the conditions of the agreement," a security source told AFP.
State television said: "The terrorist groups violated the agreement and tried to smuggle heavy weapons and hostages from east Aleppo."
The International Committee of the Red Cross, which has supervised the evacuation, confirmed it was on hold.
"The regime and its militias... Stopped the evacuation operation in another attempt to involve Fuaa and Kafraya," said Yasser al-Youssef of the Nureddin al-Zinki rebel group.
The Shiite-majority villages in Idlib province have been besieged since 2015.
The government and its other main ally Iran have reportedly sought to add an evacuation of civilians from the villages to the terms of the Aleppo deal.
The Syrian Observatory for Human Rights, a Britain-based monitor, also said the suspension appeared to be related to the two villages.
The evacuation of the last pocket of rebel territory in Aleppo began on Thursday under a deal brokered by Russia and Turkey.
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