The Tunisian news agency says a four-member border patrol was kidnapped by an armed Libyan group but three of the guards quickly escaped.
It was the first such incident along the border, which has been well guarded since the violent uprising that left Moammar Gadhafi dead in October.
The TAP agency cited the Interior Ministry on Sunday as saying that the four were kidnapped a day earlier in the Ben Guerdane region and three quickly escaped.
It did not confirm a Mosaique radio report that the fourth guard was freed Sunday morning and was to be treated at a Tunis hospital for a bullet wound.
Ministry spokesman Hicham Meddeb says "certain parties" were trying to trouble ties ahead of a trip this week to Libya by Tunisia's new president, Moncef Marzouki.