The Wilayat Tripoli ("State of Tripoli") group said on Twitter that its fighters had kidnapped 21 Copts in Tripoli.
The group posted an online video of the abductees, one of whom appeared to be Egyptian.
In the Upper Egyptian province of Minya, the families of some of the abductees said they had recognized their abducted relatives from the video.
There has been no comment from Libyan authorities on the claim.
Last week, Egypt's state-run news agency quoted Libyan journalist Malik al-Sharif as saying that militants had kidnapped 13 Egyptian Copts in the coastal city of Sirte, currently under the control of the "Dawn of Libya" Islamist militia.
The latest abductions come after seven Copts were kidnapped in the city a few days earlier.
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, often bringing violence to the country's main cities, especially capital Tripoli and Benghazi.