Assange, who has been holed up in the Ecuador embassy in London for two years to avoid extradition to Sweden, is wanted for questioning there over alleged sex crimes.
On Thursday he lost his claim that the detention order be set aside.
Quito reiterates "that the asylum granted to Julian Assange is valid and reaffirms its intention to continue protecting him as long as necessary, until he is in a safe place," Ecuador's Ministry of Foreign Affairs said in a statement.
Swedish prosecutors want to question Assange about accusations of rape and sexual molestation brought against him by two women in their 30s when he visited the country in 2010. He denies the claims.
Assange had called on Swedish prosecutors to travel to London to question him or, alternatively, to do so by video link, but the appeal court rejected the demand, AFP reported.
"Ecuador maintains its proposal for Swedish officials to question Julian Assange in its embassy in London or use videoconferencing means," the ministry reiterated.
Assange fears extradition to Sweden could lead to him being transferred to the United States to face trial over WikiLeaks' publication of classified US military and diplomatic documents.
In 2010, WikiLeaks began publishing 250,000 American diplomatic cables and 500,000 classified military reports, covering both American diplomacy and the US wars in Iraq and Afghanistan.