Edward Snowden has withdrawn his request for political asylum from Russia, the Kremlin said on Tuesday, further adding to the uncertainty over the US whistleblower's future.

A spokesman for Russian president Vladimir Putin said Snowden withdrew the request after Putin's statement making clear that he would be welcome only if he stopped "his work aimed at bringing harm" to the United States.

"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, charged under espionage laws in the US after leaking top-secret documents on US surveillance programmes. He has been kept hidden away since 23 June, when he landed in Moscow's Sheremetyevo airport from Hong Kong.

His attempts to win asylum have been fraught with difficulty. Rafael Correa, president of Ecuador, told the Guardian that his country, whose London embassy is sheltering WikiLeaks founder Julian Assange, was not considering Snowden's asylum request.

He also said Ecuador never intended to facilitate Snowden's flight from Hong Kong, calling his London consul's decision to issue temporary travel documents to Snowden "a mistake".

Speaking to Reuters in Moscow on Tuesday on the second day of a two-day visit, Nicolás Maduro, the Venezuelan president, said Snowden "deserves the world's protection".

He said Venezuela had not yet received an asylum request from Snowden. Asked whether he would take Snowden back to Venezuela with him, Maduro answered wryly: "What we're taking with us are multiple agreements that we're signing with Russia, including oil and gas." But he added his support for the US whistleblower: "Edward Snowden is a 29-year-old young, brave man who didn't kill anyone, didn't give any reason for the start of war," Russian news agencies cited Maduro as saying.

A WikiLeaks statement released early on Tuesday said that in addition to Ecuador and Iceland, Snowden had made asylum requests to 19 countries, including Venezuela, China, Bolivia, France and Germany.

Maduro said Venezuela would examine the asylum request once it was received. "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," he said.

At least two countries where Snowden requested asylum have said they will not co-operate. Radoslaw Sikorski, the Polish foreign minister, said Snowden's request did "not meet the requirements for a formal application for asylum. Even if it did, I will not give a positive recommendation."

Finland said on Tuesday that it could not accept his application as Finnish law required him to be in the country. Finnish foreign ministry spokeswoman Tytti Pylkko said Snowden had sent his request by fax to Finland's embassy in Moscow.

Peskov did not detail how Snowden withdrew his asylum request from Russia. The request was handed to a Russian consular official at Moscow's Sheremetyevo airport late on Sunday via Snowden's WikiLeaks handler, Sarah Harrison.

In an awkwardly phrased 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 with his Russian counterpart, Sergey Lavrov on Tuesday on the sidelines of a summit of the Association of South-east Asian Nations (Asean) on Tuesday. Lavrov told reporters that the two did not discuss Snowden.

• According to WikiLeaks, Snowden has requested asylum from Austria, Bolivia, Brazil, China, Cuba, Ecuador, Finland, France, Germany, Iceland, India, Italy, Ireland, the Netherlands, Nicaragua, Norway, Poland, Russia, Spain, Switzerland, Venezuela.