City officials advised drivers to spend the night along the route unless they were close to Zaporizhzhia by evening.
No fewer than 400 people are being held hostage by Russian troops after occupying an intensive care hospital in the Mariupol, a Ukrainian city.
This was made known on Tuesday by Donetsk Oblast Governor, affirming that Russian forces "drove 400 people from neighbouring houses to the hospital and they can’t leave," according to LBC.
"It is impossible to get out of the hospital. There is a heavy shooting; we sit in the basement,” Pavlo Kirilenko, head of the Donetsk regional military administration, said.
"Vehicles have not been able to drive to the hospital for two days. High-rise buildings are burning around. Russians forced 400 people from neighbouring houses to come to our hospital. We can't leave."
Russian forces were said to be apparently firing at the windows of the hospital in an effort to trigger a response from Ukrainian soldiers, according to the Media Initiative for Human Rights.
The human rights organisation said the Russian military are "threatening to shoot" at hostages who attempt to escape adding that "patients who risked to escape from captivity returned with bullet wounds.”
According to the report, Pavlo Kyrylenko said Russian invaders "practically destroyed" the hospital in previous days but hospital staff and patients continued to carry out emergency work in the basement.
"The destruction was not enough for Russian villains – now they made people hostages.
"I appeal to international human rights organizations to respond to these vicious violations of the norms and customs of war, to these blatant crimes against humanity. Russia and its every citizen involved in crimes in Ukraine must be punished."
Some 2000 civilian vehicles left the besieged Ukrainian port city of Mariupol on a so-called humanitarian corridor on Monday, the city council says.
The city council said another 2,000 cars were waiting to leave along the evacuation route, which runs west for more than 160 miles to the Ukraine-held city of Zaporizhzhia.
City officials advised drivers to spend the night along the route unless they were close to Zaporizhzhia by evening.
Mariupol had a population of 430,000 before the war. The strategically located city has been under fire for more than two weeks.
Officials estimate the siege had killed more than 2,300 people and said it had left residents desperate for food, water, heat and medicine.