The Egyptian workers were taken at gunpoint from a housing complex in the city of Sirte in the early hours of Saturday morning.
Eyewitnesses say Islamist militants were to blame and that the gunmen separated the Christians from the Muslims.
But authorities rejected this and claimed they were taken by people traffickers.
Head of the council of elders in Sirte said a deal had been done to secure the release of the 13 men.
"The Egyptians were held by a group that deals in illegal people smuggling, because of a dispute involving money and transportation to the Harawa region east of Sirte," he said.
The kidnappings were the latest in a number of violent attacks on Christians in Libya.
Last week seven other Coptic Christians from Egypt were abducted at a fake checkpoint as they tried to return home.
These men are still thought to be missing.
His Grace Bishop Angaelos, General Bishop of the Coptic Orthodox Church in the United Kingdom said: "It is deeply concerning to witness the unprovoked, targeted and escalating attacks on Egyptian Coptic Christians in Libya, particularly but not exclusively in Sirte.
"In recent years Coptic Christians in Libya have endured horrific acts of brutality that include the bombing of churches, abductions, torture, and execution style murders.
"Out of serious concern and in light of these circumstances a meeting is currently being sought with the Libyan Ambassador to Britain for further discussion of these constantly evolving events.
"At a time when Coptic and other Christian families are preparing to celebrate the Feast of the Nativity, we pray for those who are literally concerned for their lives in Libya as well as for countless other Christians and minority groups across the Middle East who are victims of war, violence, and unrest."
Bishop Angaelos, General Bishop of the Coptic Orthodox Church, United Kingdom:
Video Has not been found