Rescue crews in Istanbul and Athens have cleared roads that had come to a standstill after a massive cold front and snowstorms hit much of Turkey and Greece, leaving countless people and vehicles in both cities stranded overnight in freezing conditions.

Roads in and around Istanbul became clogged on Monday after the storm pounded the city of about 16 million people that straddles the European and Asian continents — accumulating more than 80cm (31in) of snow in some areas.

Stranded motorists spent the night in cars, abandoned their vehicles to walk home or crowded subways and other public transport.

All motorways and main roads were reopened by Tuesday afternoon, transportation minister Adil Karaismailoglu announced on Twitter, while Istanbul governor Ali Yerlikaya said restrictions placed on vehicles traveling into Istanbul had been lifted.

Authorities also cleared a runway at Istanbul Airport on Tuesday, allowing limited flights to resume. Flights were suspended on Monday for safety reasons at the airport, where the roof of a cargo facility collapsed from the weight of the snow.

Hundreds of passengers stranded at Istanbul Airport shouted “we need (a) hotel” in protest at their ordeal, Cumhuriyet newspaper reported.

In Athens, rescue crews freed around 200 to 300 drivers who were trapped on a major motorway that runs across Athens and connects the Greek capital with the city’s international airport.

The army was sent out overnight to deliver food and water to those trapped and to help free as many as possible.

The heavy snow had mostly stopped on Tuesday, but many streets in Athens remained blocked by trees whose branches snapped under the weight of the snow.

Several neighbourhoods in the Greek capital, particularly in the northern part of the city, remained without power.

Authorities had ordered all but essential public and private businesses shut on Tuesday, and have extended that for Wednesday as well in the wider Athens area and several other regions of Greece.

Istanbul’s Disaster Co-ordination Centre (AKOM) said an Icelandic low-pressure system was behind the cold front and precipitation affecting most of the country.

Rescue teams in the city worked overnight to clear snowy roads, but abandoned vehicles hampered their operations.

Interior minister Suleyman Soylu said the snow in and around Istanbul would continue until Thursday and urged people not to venture out in private cars unless necessary.

Authorities in Greece had warned people to limit their movements to the essential and to use snow chains on city streets, but many people had set out for work in the morning when the snowfall was much lighter and became trapped in their cars as the day wore on.

Some of the problems were reportedly caused by trucks that slipped and jack-knifed across the road, blocking traffic.

The snowstorm, complete with thunder and lightning, hit the wider Athens area late in the morning on Monday, dumping large amounts of snow on the city.

Last year, similar weather in February left tens of thousands of trees felled by the weight of the snow on city streets, parks and woodland around Athens.

Officials said the Greek prime minister contacted the highways administration and asked for each trapped driver to receive 2,000 euros (£1.673) in compensation, which the agency accepted.

“It was a very difficult night and we faced unprecedented conditions,” civil protection and climate change minister Christos Stylianides said. “I want to again express an apology from the state for all the difficulties that the (stranded) drivers faced.”

The severe weather also brought rare snow to holiday resorts in Turkey’s south west, including Bodrum and Datca, with snow and slippery conditions blocking a motorway linking the provinces of Mugla and Denizli.

Antalya city centre, on the Mediterranean coast, had its first snowfall in 29 years, NTV television reported.