Ricardo Alarcon accuses the US of the "privatisation of war"
Washington has labelled "false" Cuban claims that an American contractor arrested at Havana airport last month was a US spy.
The US state department said the man did not work for American intelligence.
Earlier, Cuban Parliament President Ricardo Alarcon said the unnamed man was still under investigation and had not been charged.
The BBC's Michael Voss says the incident suggests US-Cuba ties have again taken a turn for the worse.
Relations between the two countries had started to thaw after US President Barack Obama came to office in January last year.
"Those comments are false. Cuba has a history of mischaracterising what Americans and NGOs in Cuba are doing," said state department spokesman PJ Crowley.
"This person is not associated with our intelligence services."
Washington said the detained man worked for an American company called Development Alternatives, part of a US government programme aimed at promoting civil society and democracy in Cuba.
The American was held at Havana airport on 5 December but was not seen by US consular officials until 28 December.
"This is a gentleman hired by a company that hires for the American secret services and is now the subject of an investigation," Mr Alarcon told reporters in Havana.
He described it as an example of the "privatisation of war" by the US, which hires people to be "agents, torturers, spies".
In an earlier speech, President Raul Castro said the man had been illegally supplying opposition groups with advanced communications equipment.
He also accused the US of continuing its attempts to subvert and destroy the revolution, our correspondent in Havana reports.