He has been in the Ecuadorian embassy in London since June 2012, claiming political asylum in order to escape a European Arrest Warrant over the claim.
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 a court document seen by Reuters, chief prosecutor Marianne Ny said there were no further avenues to pursue to take the investigation forward.
Attorney General Jeff Sessions has suggested that the arrest of Assange could be an American priority, saying last month the USA was "stepping up our efforts on all leaks".
British police said despite Sweden's decision to drop a rape investigation, Assange still faces arrest if he leaves Ecuador's embassy in London.
WikiLeaks tweeted after the Swedish announcement: "UK refuses to confirm or deny whether it has already received a United States extradition warrant for Julian Assange".
Ms Ny said the investigation could have progressed if Mr Assange was "formally served notice of the crimes of which he is suspected", adding: "This was a measure which was to have been conducted during the interview in London but Mr Assange refused to make it possible".
It raised developments in the USA since the election of Donald Trump as President, including a speech by CIA director Mike Pompeo describing WikiLeaks as a "hostile intelligence service".
The Swedish Prosecution Authority said in a statement Friday that Marianne Ny "has chose to discontinue the investigation".
Ny told reporters that prosecutors had been unable to make a full assessment of the case and were not making a finding on whether Assange was guilty or innocent of the allegations. British Prime Minister Theresa May said Friday that "any decision that is taken about United Kingdom action in relation to him (Assange) would be an operational matter for the police". He has been there ever since, fearing that if he is arrested he might ultimately be extradited to the United States.
Samuelson said he did not know if Assange would leave the embassy building in London and try to go to Ecuador.More news: Celtics win National Basketball Association draft lottery, Lakers at No. 2 keep pick
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", the group tweeted.
Scotland Yard said it was obliged to execute a warrant issued by Westminster Magistrates' Court for the arrest of Mr Assange following his failure to surrender to the court in June 2012, should he leave the embassy.
Mr Assange has denied that he was given the leaked documents by Russian Federation, although he has refused to say where he got them.
British officials said they do not comment on individual extradition cases.
WikiLeaks also had a role in the 2016 USA presidential campaign when it published emails written by Hillary Clinton's campaign officials.
A defense lawyer acting for Assange, Per E. Samuelsson, told Swedish Radio the decision to drop the rape charges is "a total victory for us." .
He said American officials made up the case in an attempt to have him extradited.
"We will seek to put some people in jail", Sessions said.
However if Assange were to return to Sweden before the statute of limitations for the suspected offenses expires in August 2020, the investigation could be reopened, she said. "My client is shocked and no decision to (end the case) can make her change that Assange exposed her to rape".
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.
Police kept up round-the-clock guard outside the embassy until previous year, when the operation was scaled back.