TUNIS/TRIPOLI – The wife and daughter of Libyan leader Muammar Gaddafi crossed the border into Tunisia, a Tunisian security source said, but it was unclear whether they were on a diplomatic mission or seeking safe haven.

Arabic television stations quoted Tunisian officials as denying that the family members were in the country, saying that Safia Gaddafi and her daughter Aisha were on a UN sanctions list and would therefore not be allowed in.

However, the security source said the two women came to Tunisia with a Libyan delegation on May 14 and have been staying on the southern island of Djerba near the Libyan border.

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It did not appear that they were traveling with Shokri Ghanem, Libya's top oil official, who is believed to have also crossed into Tunisia several days ago and defected.

Government officials in Tripoli were not immediately available for comment.

The Tunisian Interior Ministry denied that any members of the Gaddafi family were in the country in remarks to Al Jazeera and Al Arabiya TV.

Al Jazeera quoted a ministry spokesman as saying Tunisia would arrest any members of the Gaddafi family should they enter the country under a UN-imposed travel ban.

A Libyan opposition source said the women were in Djerba to accompany Aisha's husband, who he said had been injured in the Libyan conflict, and was seeking treatment in Tunisia.

A commentator on a daily political talkshow on state-run Libyan TV dismissed reports Gaddafi and members of his family had left Libya as "rumors" and "psychological war" spread by rebels and the West.

"Those people (Gaddafi and his children) live among other people and if any of those rumors were true it would be possible to find this out," the commentator said.

Italian officials have speculated that Gaddafi, who has been in power for four decades, was wounded during a NATO air strike in the capital last month which killed his youngest son and three of his grandchildren.

Libyan television has shown footage of the leader since the bombardment and aired an audio message in which he taunted NATO forces, saying he was in a place where their artillery could not reach him.

Since the revolt began in February against Gaddafi's rule, Aisha Gaddafi has made several public appearances backing her father, and attacking the rebels and Western powers trying to overthrow him.

A month ago she appeared at her father's Bab al-Aziziyah compound in Tripoli and addressed cheering crowds of supporters in an event broadcast live on Libyan state television.

"Talk about Gaddafi stepping down is an insult to all Libyans because Gaddafi is not in Libya, but in the hearts of all Libyans," she said.

On Tuesday, Libyan rebels and a Tunisian security source said the head of Libya's National Oil Corporation, Shokri Ghanem, had defected and fled to Tunisia. If confirmed, the defection would undermine Gaddafi's efforts to cling to power.

Ghanem would be the most senior Libyan official to defect since former foreign minister Moussa Koussa switched sides in Britain earlier this year after passing through Tunisia.