MEXICO CITY, April 19 (Reuters) - A major reform bill to increase competition in Mexico's phone and television markets, dominated by Carlos Slim's America Movil and Emilio Azcarraga's Televisa, was approved by the Senate in the early hours of Friday with some changes. Senators early on Friday made a change that will allow companies to suspend, pending appeal, fines or orders issued by Mexico's competition authority. That waters down the initial bill, which sought to put an end to companies using Mexico's byzantine legal system to fight regulatory decisions. Still, companies will not be able to appeal decisions made by the proposed new telecom regulator, which also has powers to fine and order asset sales by companies, lawmakers said. The bill, the first major reform from President Enrique Pena Nieto who took office in December, will now return to Mexico's lower house for approval. Four senate commissions on Thursday approved the reform, which defines dominant players as those controlling more than half of their respective markets. Uncertainty over the final details of the bill has been dragging on the share prices of America Movil and Televisa. Slim's America Movil controls some 80 percent of the fixed line business and around 70 percent of the mobile market. Televisa has more than 60 percent of the TV market. America Movil shares are down more than 16 percent, while Televisa shares have fallen almost 9 percent this year.