"The 13 Egyptians have been moved to a secure location and will be asked whether they want to stay in Libya or return home," Muftah Marzouq, leader of Sirte's council of elders, told The Anadolu Agency.
He said the hostages had been held by human traffickers after a dispute over money paid for helping them leave the violence-prone city.
"The recent killing of a Christian family has prompted many Christians to try and flee the city – sometimes using traffickers – in fear of their lives," he said.
On Saturday, Egypt's state-run news agency quoted Libyan journalist Malik al-Sharif as saying that militants had kidnapped 13 Egyptian Copts in Sirte, which is currently under the control of the Dawn of Libya Islamist militia.
The recent abductions came a few days after seven Copts were kidnapped in the city last week.
In recent years, armed attackers believed to belong to Islamist militant groups have occasionally targeted Christians – mostly Egyptian nationals – leaving many dead and injured.
Libya has been dogged by political instability since the 2011 ouster and death of long-ruling strongman Muammar Gaddafi.
Ever since, rival militias have frequently locked horns, bringing violence to the country's main cities, especially capital Tripoli and Benghazi.