The government did not specify which currency it planned to get rid of.
But the official newspaper Granma said that the government's first step would be to allow several businesses that currently accept only convertible pesos, known by their Spanish acronym as CUC, to do business in ordinary Cuban pesos, or CUP.
The official exchange rate of 24 ordinary pesos to the dollar will remain in effect, Granma said, meaning the goods themselves will remain out of reach for Cubans without access to the foreigner exchange-driven economy, which includes millions of dollars a year in remittances from relatives in the United States and other countries.
"Experimentally, in select locations, cash payments in CUP will be allowed to take place," the paper wrote.
The double monetary system was established in 1994 amid an economic crisis sparked by the fall of the Soviet Union, which heavily subsidized Cuba for decades.
Cuba has said virtually nothing about how it will adjust the two currencies' exchange rates to prevent economic shocks. Granma assured readers that "the confidence of people who have maintained their savings in Cuban banks, in CUC, in other international currencies and CUP, will remain intact" and government subsidies of basic goods and services including food staples would continue.
Employees of a Havana bank that deals mostly with convertible pesos told The Associated Press Tuesday that they had recently received training in how to conduct more transactions with ordinary pesos, although they had not been told when they would put that training into effect.
Cubans on the streets of the capital said they welcomed the government announcement but saw it as a slow and incremental move toward broader change.
"For the moment I don't see any great changes. It'll take a while for us to end up with a single currency," said state worker Manolo Rivera, 49. "They are taking a first step toward establishing and formalizing it."
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Correspondents Andrea Rodriguez and Michael Weissenstein contributed to this report.