An investigation into a molestation charge however remained open against the 39-year-old Australian whose whistleblower site is in coming weeeks set to unveil thousands more secret documents about the war in Afghanistan.
Assange and his aides claimed he was the victim of dirty tricks, with a Twitter message attributed to the former hacker saying "The charges are without basis and their issue at this moment is deeply disturbing."
"Chief prosecutor Eva Finne has come to the decision that Julian Assange is not suspected of rape," said a statement on the Swedish prosecution service's own website, just hours after the warrant was issued.
It said that Assange was "no longer wanted."
The statement said Finne would make no other comments on Saturday, while the prosecution service referred a telephone inquiry from AFP to the website.
But Swedish prosecution office spokesperson Karin Rosander later told AFP that the investigation into a second allegation of molestation "is still open" and that "the prosecutor in charge would comment later" on the matter.
Rosander had said earlier Saturday that Assange "was wanted for two different issues, one of them is that he's suspected of rape in Sweden," while the other was the molestation charge.
AFP was unable to reach Assange directly, but one of his colleagues, Kristinn Hrafnsson, said by telephone from Iceland earlier "Julian denies these allegations and says they are false."
She said Assange was still in Sweden and knew nothing of the claims until he read about them in the Swedish daily Expressen, which broke the story.
"There are powerful organisations who want to do harm to WikiLeaks," she said.
Assange had been in Sweden earlier this month giving a press conference on the upcoming release of the last batch of Afghanistan documents, but he generally remains on the move around the world staying with supporters.
WikiLeaks had said in a statement on its blog that it was "deeply concerned about the seriousness of these allegations."
"We the people behind WikiLeaks think highly of Julian and he has our full support. While Julian is focusing on his defenses and clearing his name, WikiLeaks will be continuing its regular operations," it said.
A Twitter comment carried on the Wikileaks website said "We were warned to expect 'dirty tricks'. Now we have the first one."
Prosecutor Maria Haljebo Kjellstrand had earlier told the TT news agency that the rape was allegedly committed at Enkoping, near Stockholm, and an assault on another woman in the capital.
In another statement carried on the website of the Swedish daily Dagens Nyheter, Assange was quoted as asking why the accusations had surfaced now. "It's an interesting question," he added.
Last week Assange announced in Stockholm that the whistleblower website was set to publish the final batch of 15,000 secret documents on the war in Afghanistan in "a couple of weeks."
He insisted WikiLeaks "will not be threatened by the Pentagon or any other group."
The Pentagon for its part has said it would not negotiate a "sanitised" release of the documents, as Wikileaks had suggested it might.
WikiLeaks has already released nearly 77,000 secret papers, sparking charges that it had endangered the lives of informants and others named therein.
The website says it had repeatedly asked the Pentagon for help analysing the remaining documents, and Assange said at the weekend he wanted to avoid publishing the "names of innocent parties that are under reasonable threat," but he needed help.
US Defense Secretary Robert Gates has pronounced WikiLeaks "guilty" on moral grounds for releasing the documents and accused the website of recklessness.
General David Petraeus, the top US military commander in Afghanistan, blasted the release as "reprehensible" and said Wikileaks had placed people working with the international forces at risk.
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