BENGHAZI, Libya (Reuters) - A Tunisian woman who Libyan authorities said they had arrested and was married to veteran Algerian militant Mokhtar Belmokhtar is not his wife, her sister and an al Qaeda source have told local media.

East Libya's counter-terrorism department said they had detained the woman, identified as Asma Kadoussi, after she had traveled to the northeastern city of Derna to give birth to a child.

They said she had been living with Belmokhtar in the Libyan desert region of Jufra, suggesting that Belmokhtar, a major militant figure in the region who was targeted by a U.S. air strike in Libya in June 2015, was still alive.

Belmokhtar's fate following the air strike has never been confirmed, though the group he leads, Al-Mourabitoun, claimed he had survived.

However, a senior figure from Al Qaeda in the Islamic Maghreb (AQIM) was quoted on Saturday by Mauritania's Alakhbar news agency as saying that Belmokhtar had no Tunisian wife. Belmokhtar is a former member of AQIM and Alakhbar regularly publishes news from Islamist groups operating in the region.

Kadoussi's sister, Olfa, told Tunisian radio station Karama FM that her sibling was in fact married to a Tunisian with a similar name. "I deny that my sister is the wife of the Algerian Mokhtar Belmokhtar," she said. "Her husband is Tunisian and is called Mokhtar Ben Mokhtar Akouri."

Mokhtar Ben Mokhtar Akouri is listed by the Tunisian interior ministry as a terrorism suspect from Sidi Bouzid, the same town that Kadoussi is from.

An identity card for Kadoussi released by east Libya's counter-terrorism department also showed her married name as Akouri, and various family documents published by local media appeared to confirm that the two were married.

Tunisian authorities have declined to comment, while authorities in east Libya have continued to insist that the woman they arrested confessed she was married to the Algerian militant.

(Reporting by Aidan Lewis and Ayman al-Warfalli; Writing by Aidan Lewis; Editing by Mark Trevelyan)