He sought asylum at the embassy over fears that if he is extradited to Sweden he would be sent onward to the US for prosecution over WikiLeaks' publication of secret documents, including thousands of USA diplomatic cables.
In documents filed Friday to the Stockholm District Court, Ny wrote that "in view of the fact that all prospects of pursuing the investigation are now exhausted, it appears that, in light of the views expressed by the Supreme Court in its assessment of the proportionality in this case, it could be argued that it becomes less proportionate to maintain the arrest of Julian Assange in his absence via a European Arrest Warrant".
United States authorities have prepared charges to seek his arrest, U.S. officials familiar with the matter told CNN last month.
The Australian activist sought asylum in the Ecuadorian Embassy while on bail in 2012, over fears the Swedish investigation would result in him being extradited to the United States over leaked military documents and diplomatic cables.
WikiLeaks tweeted: "UK refuses to confirm or deny whether it has already received a U.S. extradition warrant for Julian Assange".
The long-running case against Mr. Assange had suffered several setbacks.
Sweden drops Assange investigation, UK police says he still faces arrest
In documents filed to the Stockholm District Court, Prosecutor Ny said legal obstacles had prevented the case from moving forward. Meanwhile, Ecuadorian Foreign Minister Guillaume Long urged Britain to "grant safe passage" out of the country to Assange.
Swedish Chief Prosecutor Marianne Ny said the investigation had not been able to proceed because of legal obstacles. He did not take shouted questions from the reporters assembled outside and would not say if he plans to leave the embassy located in the posh Knightsbridge neighborhood.
"Westminster Magistrates' Court issued a warrant for the arrest of Julian Assange following him failing to surrender to the court on the 29 June 2012", the police said.
British police said separately that it was still under obligation to arrest Assange were he to leave the embassy.
At a press conference in Quito, Long called on Britain allow Assange safe passage so he could take up his asylum in Ecuador. "Focus now moves to United Kingdom".
However, London police issued a statement after the Swedish announcement making clear Assange was still wanted by them.
The allegations surfaced after two women accused Assange of sexual misconduct during a visit to Stockholm in 2010.
Assange is wanted by British police for extradition to Sweden.
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"We have won the case", Assange's Swedish defence attorney Per E Samuelson told Swedish Radio, shortly after Ny's announcement.
"Now that all appeals are exhausted I expect that the United Kingdom and Sweden will comply with their global obligations and set me free", Mr Assange said following the ruling.
WikiLeaks also had a role in the 2016 US presidential campaign when it published emails written by Hillary Clinton's campaign officials.
British officials said they do not comment on individual extradition cases. There were initially two separate allegations being investigated, but one was dropped in 2015 because the statute of limitations ran out.
The preliminary investigation on Assange, 44, was opened in 2010.
Russia's role remains the subject of multiple investigations by congressional intelligence committees and the FBI, which has said it's looking into whether any associates of Trump had contact or colluded with Russian government operatives.
British police kept up round-the-clock guard outside the embassy until December 2015, when the operation was scaled back, in part because of the cost, which had exceeded 11 million pounds (over $17.5 million at the time).
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Towards the end of his presidency, Barack Obama decided she should be freed and the former intelligence analyst was recently released from jail.