(Corrects first two paragraphs to show decision made by telecom watchdog, not competition regulator)

MEXICO CITY, Dec 21 (Reuters) - Mexico's telecom watchdog on Sunday approved AT&T Inc's $1.7 billion purchase of local cellphone company Iusacell, with unspecified conditions, a statement said.

The Federal Institute of Telecommunications said it set conditions on the deal to "avoid risks to the process of competition" in markets where Iusacell would compete with Carlos Slim's America Movil, which previously counted AT&T as a minority investor.

America Movil is Mexico's biggest mobile operator, while Iusacell is a distant third.

AT&T sold its America Movil shares in the summer, before announcing its deal with Iusacell in November.

Iusacell was previously being operated as a joint venture between Mexico's biggest broadcaster Televisa and Grupo Salinas, a holding company belonging to tycoon Ricardo Salinas.

The watchdog also said in the statement it approved Televisa's sale of its 50 percent stake in Iusacell back to Grupo Salinas, from which AT&T will then buy the operator in its entirety.

Mexico's government earlier this year implemented reforms to shake up its telecom and broadcast market by weakening the dominance of broadcaster Televisa and billionaire Slim's cellphone and fixed-line company America Movil.

(Reporting by Elinor Comlay; Editing by Christian Plumb)