Assange took refuge at Ecuador's London embassy in June as he faced extradition to Sweden over sexual assault charges, which he denies.
Ecuador yesterday granted him political asylum after the country's foreign minister, Ricardo Patino, said that he believed Assange's fears of political persecution were "legitimate".
However, the UK has said that it will not allow him safe passage out of the country and the move does not change its obligation to hand him over to Sweden.
Swedish media now reports that minister of social affairs Goran Hagglund fired a salvo of abuse at Assange on Twitter.
After Ecuador indicated that it would grant asylum on Tuesday this week, the minister tweeted about Assange: "Sick. A coward who does not dare to have his case tried by the court. If the accusations against him are true, he is a scumbag."
The outburst was part of an exchange with Swedish tabloid journalist Niklas Svensson, who initially reported that Assange was wanted for questioning by Swedish police in August 2010. He has since published a series of 'highly critical' articles about Assange.
In an interview with the Expressen newspaper yesterday, Minister Hagglund also called Assange a "pitiful wretch".
There are currently no charges against Assange in Sweden and many human rights campaigners have challenged why Swedish investigators have refused all offers to question Assange over the allegations in London, instead insisting on his extradition.
Another issue is why Australia, Assange's country of birth, has not offered him consular assistance.
The Wikileaks founder himself took a swipe at his home country's lack of action, saying: "It was not Britain or my home country, Australia, that stood up to protect me from persecution but a courageous, independent Latin American nation."
However, the Herald Sun reports that Australia environment minister Tony Burke said that consular assistance would still be offered to Assange if he asked for it.
"Julian Assange is an Australian citizen... if he wants consular support, it's offered, it's available," Burke told the Seven Network on Friday.
"The offer of consular assistance is still there."
Leading human rights lawyer Geoffrey Robertson QC, who has been advising Assange's defence, said that it may be a good time for Australia to get involved.
"The Ecuadorians have been questioning the Americans, the Swedes and the British but the obvious country, the country of Mr Assange's nationality, hasn't been involved," he told ABC TV.
"So it may be an opportunity for Australia to get involved on behalf of its national and see if it can square this circle."
Robertson said that if Australia could obtain "undertakings" from Sweden that it would free Assange to return to Australia after he was questioned, then the 41-year-old may have more faith that he won't be just handed to the US as suspected.
The UK Foreign Office has been criticised for its hard line on Assange, after it at one stage even suggested that it may enter the Ecuador embassy, which is sovereign territory, to arrest the Wikileaks founder.
But Ecuador's Foreign Minister Ricardo Patino said he hoped talks with the UK would "overcome this".
Speaking to BBC Mundo, Patino said that the UK should respect Ecuador's "sovereign decision" otherwise "we will use the alternatives under international law to demand the safe passage".
"We don't think it is reasonable that, after a sovereign government has made the decision of granting political asylum, a citizen is forced to live in an embassy for a long period," he added, referring to the fact that Assange has now been in the embassy for almost eight weeks.
Patino also suggested that "other elements" were motivating Sweden's desire to extradite Assange.
Spanish human rights lawyer Baltasar Garzon, who is also assisting Assange's defence, said that the Australian will appeal to the International Court of Justice if Britain tries to block his exit to Ecuador.
There have also been suggestions that Assange could flee the UK in Ecuador's "diplomatic bag".