HAVANA - Cuba has tested Internet access with Venezuela and Jamaica via an underwater optical fiber network, initially designed for telephone signals, the official daily Granma reported Thursday.

The laying of the optical fiber network was completed in February 2011 at an estimated cost of $70 million, but trials for its use in carrying Internet traffic began on January 10, the daily reported, citing a statement from the state-run Cuban Telecommunications Company Etecsa.

However, greater Internet access will not automatically follow after the tests are completed, the company said, dampening the hopes of many Cubans with little or no access to the web.

"It will be necessary to first invest in the domestic telecommunications infrastructure and increase the foreign currency resources needed to pay for Internet traffic," the statement said.

While Internet service is free in Cuba, it is restricted to some government institutions and certain professions, like journalists and doctors.

The average citizen is not allowed to have Internet access, though black market access is available for $40 to $120 a month or more, depending on the number of surfing hours, a fortune for many Cubans.

The government blames the United States for the lack of access, saying the US-led economic embargo prohibits Cuba from connecting to international fiber optic networks near its coasts, forcing Havana to seek Internet connection via satellite, which is both slower and more expensive.

Last week, international monitoring company Renesys detected an increase in data transmission from Cuba and attributed it to the activation of the tested network.

Renesys said, however, that transmission levels had not reached levels that indicate the cable was handling all the traffic, and concluded outgoing data was still travelling via satellite.

The network, telecommunications system ALBA-1, which has been carrying telephone signals since August 2012, is expected to speed up data transfer by 3,000 times.