More than 200 people died and 1,000 were injured in the 7.2 magnitude quake, many of them in the town of Ercis, where dozens of buildings fell.
Tens of thousands have been sleeping outside in freezing conditions.
The death toll is expected to rise. Prime Minister Recep Tayyip Erdogan has been visiting the area.
Turkey is particularly vulnerable to earthquakes because it sits on major geological fault lines.
Two earthquakes in 1999 with a magnitude of more than 7 killed almost 20,000 people in densely populated parts of the north-west of the country.
It was followed by a series of powerful aftershocks, also centred north of Van, including two of magnitude 5.6 soon after the quake and one of 6.0 late on Sunday.
‘Screams for help’
Mr Erdogan has been visiting the affected area by helicopter.
He said that villages close to Van were the worst affected as most buildings there were made of clay bricks.
The prime minister thanked other countries for their offers of help but said Turkey could cope with the disaster on its own.
Up to 80 buildings, including a dormitory, collapsed in the town of Ercis, about 60km north of Van, while 10 fell in Van itself.
Town mayor Zulfikar Arapoglu appealed for help. “We need urgent aid, we need medics,” he said.
Ambulances, soldiers and rescue teams rushed to the town, a Reuters photographer reported from Ercis.
Survivors complained of a lack of heavy machinery to remove chunks of cement floors that had pancaked on to each other, the Associated Press reports.
Serious damage and casualties were also reported in the district of Celebibag, near Ercis.
“There are many people under the rubble,” said the local mayor, Veysel Keser. “We can hear their screams for help. We need urgent help.”
The head of Turkey’s seismology institute said hundreds of people could have been killed.
“We estimate around 1,000 buildings are damaged and our estimate is for hundreds of lives lost – it could be 500 or 1,000,” said Mustafa Erdik of the Kandilli Observatory.
Turkish seismologist Polat Gulkan told the BBC that building regulations were often ignored in Turkey.
“The enforcement of the code provisions is not at the standard that we would like to see it,” he said.
Residents of Van and Ercis have been spending the night huddled around camp fires in the open air, fearing more aftershocks.
Rescuers could be seen working by torchlight, using their bare hands and shovels.
The quake cut electricity and telephone lines and the authorities in some areas have cut gas to avoid the risk of fire.
The BBC’s David O’Byrne in Istanbul said more search and rescue teams were being sent from other parts of the country.
Hakki Erskoy, from the Turkish Red Crescent, said aid teams from the north and east of Turkey were being sent to the earthquake-hit area.
He said camps were being set up to shelter people and blankets, and that food and water were being sent, along with mobile kitchens.
Military aircraft were being deployed to help with the rescue and relief efforts, Mr Erskoy told BBC World News. BBC