CORRECTED - UPDATE 2-Mexico says could regulate mobile operators

(Corrects currency in last paragraph to dollars from pesos) (Adds commission calling for tariff cuts; impact on shares)

MEXICO CITY, June 16 (Reuters) - Mexico's competition watchdog ruled on Monday that all mobile phone operators in the country could be subject to more regulation of prices and practices to prevent abuse of their power over consumers.

The Federal Competition Commission named America Movil's (AMXL.MX: Quote, Profile, Research) (AMX.N: Quote, Profile, Research) Telcel network, Telefonica's (TEF.MC: Quote, Profile, Research) Movistar unit, Iusacell and Unefon as the companies that could see more regulation in the sector.

In its preliminary findings of a probe into call completions, the commission said all operators wielded "substantial power" in the completing of calls to their networks.

"Each operator has the capacity, unilaterally, to restrict calls to their network," the commission said.

Once a definitive ruling is given, authorities could regulate the market to "avoid the abuse of this power in detriment of the efficiency of the markets and the welfare of consumers," the commission said.

The commission wants mobile operators to reduce the high tariffs they charge competitors for completing calls, a commission source said on Monday.

Shares of America Movil, controlled by billionaire tycoon Carlos Slim, fell 0.31 percent to 29.09 pesos. The company's New York traded stock was down 0.64 percent to $56.23. (Reporting by Chris Aspin; Editing by Braden Reddall)