It was not immediately clear whether further evacuations were taking place on Sunday. It came as shells fired by the Islamic State group on government-held parts of the eastern city of Deir el-Zour wounded two members of a Russian media delegation visiting the area, according to state-run Syrian news agency SANA.
The convoy was carrying residents and pro-government fighters from the Shi'ite villages of al-Foua and Kefraya, which are besieged by rebels in nearby Idlib province, an insurgent stronghold.
Late on Saturday buses began crossing into both government-held and rebel-held territory from the two transit points as the deal resumed, pro-Damascus media and the Syrian Observatory for Human Rights monitoring group reported.
"The situation is disastrous", said Ahmed Afandar, a resident evacuated from the opposition area near Madaya. Abdurrahman said no permission was given for the evacuation to go ahead while Mahmoud said it has been delayed for "logistical reasons".
It added that the Saturday bombing complemented the USA attack on the Shayrat Airfield in Homs Province with a barrage of 59 Tomahawk missiles on April 7, which caused some 15 fatalities, including civilians.More news: Funerals held for victims of Egypt church bomb attacks
A suicide bomber lured children by handing out crisps before detonating a huge blast that killed at least 45 people in Syria, a witness said. "I can't find them", said a woman who appeared on al-Ikhbariya, weeping outside the state hospital in Aleppo where the wounded were transported.
"May [God] sustain the efforts of those who are actively working to bring comfort and relief to the civilian population in beloved Syria, who are greatly suffering from a war that does not cease to sow horror and death", Francis said.
The blast hit the Rashidin area on Aleppo's outskirts, where dozens of buses carrying mostly Shia residents of two villages that are being evacuated in a deal between warring sides were waiting to enter the city.
United Nations relief coordinator Stephen O'Brien said he was "horrified" by the deadly bombing, and that while the United Nations was not involved in the transfer it was ready to "scale up our support to evacuees".
The evacuation deal is one of several over recent months that has seen President Bashar al-Assad's government take back control of areas long besieged by his forces and their allies. Residents of Foua and Kfraya, besieged by the rebels, have lived under a steady hail of rockets and mortars for years, but were supplied with food and medicine through military airdrops.