A row has flared in Mexico after a radio station fired a journalist, who said on air that President Calderon should respond to drinking allegations.
Carmen Aristegui said the station was pressured by the presidency to make her apologise, which she refused to do.
The president's office denied any involvement in her sacking.
Officials have said rumours about Mr Calderon do not merit a response and his private secretary said that the president enjoyed good health.
The controversy began last week when a left-wing deputy unfurled a banner in Congress, alleging that Mr Calderon had alcohol problems.
Ms Aristegui, who is a well-known radio and TV host, said the accusation was serious and warranted an official response from the presidency.
On Monday she was sacked by MVS Noticias, who said they were terminating her contract because she had violated their code of ethics by "broadcasting rumour as news" and had refused to apologise.
The journalist hit back on Wednesday, telling a news conference that MVS Noticias, which is waiting to renew its broadcast licence, had come under official pressure to fire her.
"An act like this is only imaginable in a dictatorship that nobody wants for Mexico: punishing for opining or questioning rulers," Ms Aristegui said, adding that she had nothing to apologise for.
A statement from the presidency said accusations that there had been any pressure on MVS were false.
"The federal government is and has been scrupulously respectful of freedom of expression," it said.
Late on Wednesday, Roberto Gil Zuarth, Mr Calderon's private secretary, told a briefing that over the last year the president had attended on average seven events a day.
"During the four years of his administration, he has never missed any event because of health problems," Mr Gil said.
"This pace of work is the best proof of his good health, his physical strength and integrity."
Mr Calderon's work schedule was clearly incompatible with the unfounded rumours that aimed to damage the president, his family and the institution he represents, Mr Gil added.
Carmen Aristegui's sacking has been hotly debated on social networks in Mexico, the BBC's Mexico City correspondent, Julian Miglierini, says.
It has also been widely discussed in the mainstream press, with some columnists saying her sacking raises questions about the freedom of the media in Mexico.
But others have said that the allegations about Mr Calderon are malicious lies.