The allegations were made by Rio-based journalist Glenn Greenwald in a programme on TV Globo on Sunday.
Mr Greenwald obtained secret files from US whistle-blower Edward Snowden.
Communications from the Mexican president were also accessed by the NSA, Mr Greenwald said.
The US ambassador to Brazil, Thomas Shannon, was briefly summoned to the Brazilian foreign ministry, "to explain" the claims made by the American journalist.
He did not speak to reporters when he left, and there have been no comments from the foreign ministry either.
Mr Greenwald, a columnist for the British Guardian newspaper, told TV Globo's news programme Fantastico that secret documents leaked by Edward Snowden showed how US agents had spied on communications between aides of Brazil's President Dilma Rousseff.
Brazil's Justice Minister Jose Eduardo Cardozo said that "if these facts prove to be true, it would be unacceptable and could be called an attack on our country's sovereignty".
According to the report, the NSA also used a programme to access all internet content that Ms Rousseff visited online.
Her office said the president was meeting top ministers to discuss the case.
The BBC's Julia Carneiro in Sao Paulo says that the suspicion in Brazil as to why the United States is allegedly spying Brazilian government communications is because Brazil is a big player and there are lots of commercial interests involved.
The report also alleges that the NSA monitored the communications of Mexican President Enrique Pena Nieto, even before he was elected in July last year.
Mr Greenwald said that a document dating from June 2012 showed that Mr Pena Nieto's emails were being read.
A spokesman for the Mexican foreign ministry told the Agence France Presse news agency that he had seen the report but had no comment.
The documents were provided to Mr Greenwald by ex-US intelligence analyst Edward Snowden, who was granted temporary asylum in Russia after leaking secret information to media in the US and Britain.
Mr Greenwald was the first journalist to reveal the secret documents leaked by Mr Snowden on 6 June. Since then, he has written a series of stories about surveillance by US and UK authorities.
The detention last month for nine hours at London's Heathrow airport of Mr Greenwald's partner, David Miranda, caused widespread controversy in the UK and abroad.
Mr Greenwald said the detention of his partner amounted to "bullying" and was "clearly intended to send a message of intimidation" to those working on the NSA revelations.
The British government said that it was right for the police to act if they believed that someone had "highly sensitive stolen information".
Brazil says it will demand an explanation from the US after allegations that the National Security Agency (NSA) spied on Brazilian government communications.