"France cannot act on his request," said the office of President Francois Hollande in a statement, after Assange wrote an open letter to the government requesting asylum.
"The situation of Mr Assange does not present an immediate danger. Furthermore, he is subject to a European arrest warrant," Hollande's office said.
In his letter to the president, published earlier today in Le Monde newspaper, Assange described himself as a "journalist pursued and threatened with death by the United States' authorities as a result of my professional activities".
He also raised the issue of US spying on French leaders, which caused controversy last week when WikiLeaks released documents indicating that the United States had wiretapped Hollande and his two predecessors.
"The scale of the scandal and the reactions that followed our latest revelations confirmed the legitimacy of our approach," he wrote.
"These revelations were made at the risk of our lives."
Assange has spent over three years holed up in the Ecuador embassy in London to avoid extradition to Sweden, where he faces allegations by two women, one of rape and one of sexual assault, which he denies.
In his letter to Hollande, Assange said he had not seen his youngest child or the child's mother - both French - for five years.
"I have had to keep their existence secret up to today in order to protect them," he wrote.
He claimed last month that Swedish prosecutors had cancelled a long-awaited interview regarding his case.
Prosecutors had long insisted that he travel to Sweden for questioning but in March they agreed to go to London because some of the alleged offences will reach their statute of limitations in August.
A criminal investigation is ongoing in the US into WikiLeaks' release in 2010 of 500,000 classified military files on the wars in Afghanistan and Iraq and 250,000 diplomatic cables.
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