A Chadian army unit intercepted the GSPC members in the northern Tibesti region, near the border with Libya, on Monday and engaged them in combat, a source close to Chad's military said on Tuesday.
The fighting was still raging on Tuesday, he said. The GSPC, set up in 1998 and which last year declared its allegiance to Usama Bin Ladin's al-Qaida network, is on Washington's list of "terrorist organisations".
It is the larger of two hardline Islamic groups still fighting the Algerian government in a civil war that broke out in 1992 and has since claimed about 100,000 lives.
The GSPC was also behind the kidnapping last year of 32 European tourists in southern Algeria, some of whom it held hostage for six months.
A first group of hostages was released in May, when the Algerian army raided the kidnappers' hideout near the border with Libya, but a second group was made to trek across the desert into Mali, and was only released in August, allegedly after a hefty ransom was paid to the GSPC.