The UK has said it will not allow him safe passage out of the country.
Ecuador's Foreign Minister Ricardo Patino said he hoped talks with the UK would "overcome this".
He told BBC Mundo 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.
Ecuador says Mr Assange's human rights might be violated if he is sent to Sweden to be questioned over allegations that he sexually assaulted two female ex- Wikileaks volunteers while he was in Stockholm to give a lecture in 2010.
The Wikileaks website has published a mass of leaked diplomatic cables that embarrassed several countries, particularly the US.
The 41-year-old Australian citizen, who claims the sexual contact was consensual, says the allegations against him are politically motivated and he fears that, if extradited to Sweden, he will then be passed on to US authorities.
The UK Foreign Office says it remains committed to reaching a "negotiated solution" but following its obligations under the Extradition Act, it would arrest Mr Assange if he left the embassy.
UK Foreign Secretary William Hague said there was "no legal basis" to allow Mr Assange safe passage out of the country and warned that the case could go on for a "considerable" time.