Edward Snowden has offered to help Brazil investigate US spying on its soil in exchange for political asylum, in an open letter from the NSA whistleblower to the Brazilian people published by the Folha de S Paulo newspaper.

"I've expressed my willingness to assist where it's appropriate and legal, but, unfortunately, the US government has been working hard to limit my ability to do so," Snowden said in the letterwrote.

"Until a country grants me permanent political asylum, the US government will continue to interfere with my ability to speak out."

Senator Ricardo Ferrão, chairman of the Senate foreign relations committee, said on Twitter: "Brazil should not miss the opportunity to grant asylum to Edward Snowden, who was key to unravelling the US espionage system."

Fellow committee member Senator Eduardo Suplicy said: "The Brazilian government should grant him asylum and the US government must understand that the NSA violated rights protected in Brazil's constitution."

But a spokesman for the foreign ministry said it was not considering Snowden's appeal, because it had not yet received a formal asylum request.

In his letter, Snowden – currently living in Russia, where he has been granted a year's asylum until next summer – said he had been impressed by the Brazilian government's strong criticism of the NSA spy programme targeting internet and telecommunications worldwide, including monitoring the mobile phone of the Brazilian president, Dilma Rousseff.

Revelations of US spying have stirred outrage in Brazil. Leaked documents have shown that the NSA spied on Rousseff's emails and phone calls, tapped the communications of Brazil's biggest oil company, Petrobras, and monitored those of millions of citizens.

Rousseff has been one of the most vocal critics of the spying revealed by Snowden. In September she launched a blistering attack on US espionage at the UN general assembly, with Barack Obama waiting in the wings to speak next.

The following month, she cancelled a visit to Washington that was to include a state dinner, and she has joined Germany in pushing for the UN to adopt a symbolic resolution that seeks to extend personal privacy rights to all people.

Rousseff has also ordered her government to take measures including laying fibre-optic lines directly to Europe and South American nations in an effort to "divorce" Brazil from the US-centric backbone of the internet that experts say has facilitated NSA spying.

Brazilian senators have asked for Snowden's help during hearings about the NSA programme's aggressive targeting of Brazil, an important transit hub for transatlantic fibre-optic cables.

In his letter, Snowden used Brazilian examples to explain the extent of the US surveillance he had revealed. "Today, if you carry a cellphone in São Paulo, the NSA can track where you are, and it does – it does so 5bn times a day worldwide.

"When a person in Florianópolis visits a website, the NSA keeps track of when it happened and what they did on that site. If a mother in Porto Alegre calls her son to wish him luck with his exam, the NSA can save the data for five years or longer. The agency can keep records of who has an affair or visits porn sites, in case it needs to damage the reputations of its targets."

He added: "Six months ago, I revealed that the NSA wanted to listen to the whole world. Now the whole world is listening, and also talking back. And the NSA does not like what it is hearing."

Snowden's offer comes a day after the White House dashed hopes that the US might be considering an amnesty for the whistleblower, insisting he should still return to the US to stand trial.

Asked about weekend comments by senior NSA official Richard Ledgett suggesting that an amnesty was "worth talking about" if Snowden returned the missing NSA documents, White House spokesman Jay Carney said: "Our position has not changed on that matter – at all. He [Ledgett] was expressing his personal opinion; these decisions are made by the Department of Justice."

Also on Monday a US district judge ruled that the NSA's bulk collection of millions of Americans' telephone records probably violates the US constitution's ban on unreasonable search. The case is likely to go all the way the supreme court for a final decision. Snowden responded to that decision with a public statement that said: "Today, a secret programme authorised by a secret court was, when exposed to the light of day, found to violate Americans' rights. It is the first of many."

The Guardian first published accounts of the NSA's spy programmes in June, based on some of the thousands of documents Snowden handed over to the Brazil-based American journalist Glenn Greenwald and his reporting partner Laura Poitras, a US filmmaker.

Following the publication of Snowden's letter, David Miranda, the partner of former Guardian journalist Glenn Greenwald, started a petition on the Avaaz activist website calling for Brazil to grant asylum. Miranda wrote: "We have to thank a person for bringing us the truth and helping us fight the aggressive American espionage: Edward Snowden. He is public enemy No 1 in the US. He is someone I admire.

"Edward is running out of time. He is on a temporary visa in Russia, and as a condition of his stay there he cannot talk to the press or help journalists or activists better understand how the US global spying machine works.

"If Snowden was in Brazil, it is possible that he could do more to help the world understand how the NSA and its allies are invading the privacy of people around the world, and how we can protect ourselves. He cannot do it in Russia."

Following the extra media exposure prompted by Snowden's open letter, Michael Freitas Mohallem, the campaign director for Avaaz in Brazil, said his organisation was preparing to back the petition with a letter to all of the group's 6 million members.

"I don't see a single reason why president Dilma would say no. Snowden is a hero. He's made a sacrifice to open our eyes, particularly in Brazil. Even DIlma was involved and Petrobras. This made big news. I think Brazilian people care about it and they will stand behind Snowden," said Mohallem.

However the Ministry of Foreign Affairs has shown no inclination that it is ready to offer aslym to Snowden despite earlier campaigns by civil society organisations and social networks. One group, called Juntos, previously staged a group called Juntos outside the Ministry of Foreign Affairs, which earlier indicated a reluctance to accept a request from Snowden.

Laura Tresca from the South American office of the freedom of information group Article 19 said Brazil should grant Snowden asylum.

"Brazilian society was deeply offended by the scope of the spying he revealed through his whistleblowing. Even now, social media actors are calling him a hero without a nation," she said. "As the Brazilian Government is leading the international debate about this surveillance, it should be consistent and grant asylum to the man who made this debate possible." Miranda is currently applying for a judicial review of his nine-hour detention at London's Heathrow airport in August.