The magnitude 6.8 quake shook Elazig province, about 550km east of the capital Ankara, and was followed by more than 250 aftershocks.
Sixteen people were killed in Elazig and four more in the neighbouring province of Malatya, said Turkey's Disaster and Emergency Authority (AFAD), adding 1,030 others were injured and in hospitals in the region.
Footage early today showed emergency workers rescuing three people in Elazig after 12 hours under the rubble. Another woman in Elazig was rescued after 13 hours, while authorities listened for voices of what the government said was 30 more people still trapped.
State broadcaster TRT showed footage of dozens of workers in the dawn light using shovels to dig out a partly collapsed building in Elazig. Windows were smashed and balconies from at least four storeys had crashed to the ground.
Teams worked through the night with their hands, drills and mechanical diggers to remove bricks and plaster from the ruins in the city where the overnight temperature dipped to -8 degrees Celsius.
"Our houses collapsed ... we cannot go inside them," said a 32-year-old man from the town of Sivrice, epicentre of the quake which struck shortly before 9pm (1800 GMT).
"In our village, some people lost their lives. I hope God will help us," said the man, who gave only his first name, Sinasi.
"Our animals died. Our families gathered around the fire to spend the night, covered with blankets," Sinasi said as he and a relative tried to warm themselves by a small fire.
State media in Syria and Iran both reported the earthquake was felt in those countries. Local media in Lebanon said the cities of Beirut and Tripoli also felt the quake.
Turkish Interior Minister Suleyman Soylu described it as a "Level 3" incident according to the country's emergency response plan, meaning that it called for a national response but did not require international help.
He said Turkey, which straddles seismic faultlines and is prone to earthquakes, had learnt lessons from previous disasters which helped it address Friday's incident. Drones were deployed in search operations and communication between provinces.
AFAD warned residents not to return to damaged buildings because of the danger of further aftershocks. It said beds, blankets and tents were being sent to the area where some people sheltered in sports gymnasiums. Turkey's Kizilay aid group also sent food, heaters and other materials to the region.
"I wish God's mercy to our brothers who lost their lives in the earthquake, and urgent healing for those who were injured," President Tayyip Erdogan said on Twitter.
Turkey has a history of powerful earthquakes. More than 17,000 people were killed in August 1999 when a 7.6 magnitude quake struck the western city of Limit, 90km southeast of Istanbul. About 500,000 people were made homeless.
In 2011, an earthquake struck the eastern city of Van and the town of Ercis, some 100km to the north, killing at least 523 people. — Reuters