However, Muftah Marzuq, head of the council of elders in the coastal city of Sirte, insisted that the 13 had not been kidnapped, but had been detained by people smugglers.
"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," Marzuq said.
News of their disappearance emerged on Saturday when a source close to the government accused the Ansar al-Sharia Islamist militant group of having kidnapped the 13 Coptic Christians in Sirte.
The source said seven other Egyptian Christians had also been seized over the past few days in Libya.
Marzuq said Sirte city elders negotiated the release of the 13, without giving further details. He also did not mention the other seven.
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Thousands of Egyptians work in Libya, mainly in the construction and craft sectors.
They have been targeted as the country has descended into chaos since dictator Moamer Kadhafi was overthrown and killed in the 2011 NATO-backed uprising.
Sirte, Kadhafi's home town, is in the hands of Islamist militias including Ansar al-Sharia, which the UN last month added to its terror list over links to Al-Qaeda and for running Islamic State group training camps.
More than three years since Kadhafi's overthrow, Libya is awash with weapons and powerful militias, and it has rival governments and parliaments.
The internationally recognised government has been based in the country's remote east since an alliance of Islamist-backed militias, Fajr Libya (Libya Dawn), seized control of Tripoli in August.
In February, the bodies of seven Egyptian Christians who had been shot were found near Libya's second city Benghazi, much of which has been overrun by Islamist militias.