Edward Snowden's hopes of finding refuge from prosecution appeared to be dwindling on Tuesday as country after country denied the US whistleblower's requests to seek political asylum.

Snowden sought political asylum from 21 countries, according to WikiLeaks, passing his requests to Russian officials from his hideaway in Moscow's Sheremetyevo airport.

Several countries replied with a flat out "no", including Brazil, India, Norway and Poland. "I will not give a positive recommendation," the Polish foreign minister, Radoslaw Sikorski, wrote on his Twitter account.

A spokesman for the Indian foreign ministry tweeted: "Following careful examination, we have concluded that we see no reason to accede to the Snowden request."

To add insult to injury, Brazil said it did not feel Snowden's request deserved a response.

An enraged US has warned countries against accepting Snowden, who they are seeking on charges that he violated the espionage act when gathering and leaking classified documents outlining the National Security Agency's surveillance programmes.

Officials from many countries said Snowden would have to be on their territory to properly apply for asylum, a major stumbling block as the whistleblower has been stripped of his US passport and remains confined inside Sheremetyevo without travel documents.

He arrived in Moscow from Hong Kong last week on travel documents issued by Ecuador, but the country's officials have since rolled back their support. Rafael Correa, Ecuador's president, said on Monday that providing Snowden with those documents had been "a mistake".

"The right of asylum request is one thing but helping someone travel from one country to another – Ecuador has never done this," he said.

Ecuador was one of nearly a dozen countries that replied to Snowden's overtures by saying he would have to apply from their territory. Others include Austria, Finland, Germany, Ireland, the Netherlands, Norway, Poland, Spain and Switzerland.

The German foreign minister, Guido Westerwelle, said it would review the asylum request "according to the law", although he "could not imagine" that it would be approved

Several more countries – China, Cuba, Iceland, France, Italy and Nicaragua – have yet to respond.

Last night Bolivia emerged as one possible destination, although the president, Evo Morales, said his country had not received a request.

"If there were a request, of course we would be willing to debate and consider the idea," Morales told Spanish language RT Actualidad.

Snowden has also pinned hopes on Venezuela, whose president, Nicolas Maduro, was in Moscow this week praising his leaks on US surveillance programmes while coyly addressing his chances of asylum in Caracas.

"We think this young person has done something very important for humanity, has done a favour to humanity, has spoken great truths to deconstruct a world … that is controlled by an imperialist American elite," Maduro said.

Asked whether he would take Snowden back to Venezuela with him, Maduro answered: "What we're taking with us are multiple agreements that we're signing with Russia, including oil and gas."

Venezuela may remain Snowden's best chance after his decision to cancel his asylum request with Russia. According to Vladimir Putin's spokesman, Dmitry Peskov, Snowden cancelled the request after hearing Putin's statement that the US whistleblower would only be welcomed if he stopped "his work aimed at bringing harm" to the US.

"Snowden really asked to remain in Russia," Dmitry Peskov, the spokesman, said. "Learning yesterday of Russia's position … he abandoned his intentions and his request to get the possibility to stay in Russia."

Russia has refused to hand over Snowden, who has been hiding somewhere in Sheremetyevo airport since 23 June.

In a statement released via WikiLeaks late on Monday, Snowden accused the Obama administration of "using citizenship as a weapon" and placing undue pressure on countries where he had applied for asylum.

John Kerry, the US secretary of state, spoke to his Russian counterpart, Sergei Lavrov, on Tuesday on the sidelines of a summit of the Association of South-East Asian Nations. Lavrov told reporters that they did not discuss Snowden.

Meanwhile the whistleblower's father, Lonnie Snowden, has written an open letter praising his son for "summoning the American people to confront the growing danger of tyranny."