She said the request to Britain to accept diplomatic status for Assange was made on December 20, and denied a day later.
Ecuador has been "considering and exploring the possibility of a mediation" to resolve the issue.
U.S. Attorney General Jeff Sessions, responding to a reporter's question in April about whether arresting Assange was a priority, said it was.
Espinosa, who had already announced that the Australian journalist is in poor health, explained that no person should live such conditions as Assange, since the founder of Wikileaks has been "in a small office" for more than five years, without being able to "access sunlight or breathe fresh air".
January 17, 2017: Barack Obama, in one of his final acts as President of the U.S., decides to free whistleblower Chelsea Manning.
The newspaper said Assange may also have been given a passport.
Assange also points out that he has no limitations under the UN Convention on the Status of Refugees (1951), under which Ecuador granted him asylum.
So, is Ecuador now sick of its permanent house guest? A person can not live in these conditions forever.
WikiLeaks founder Julian Assange's name has appeared in an Ecuadorean government database of citizen identification numbers, fuelling speculation that he may have received citizenship from the Andean country.
Ecuador is hoping an global dignitary with experience in negotiations can act as a mediator, or a country not now involved in the diplomatic tussle.
The renewed demands for Assange's head came in the wake of WikiLeaks' release of almost 8,000 web pages detailing an array of classified Central Intelligence Agency hacking tools.
ANU professor of worldwide law, Don Rothwell, has been following the case closely. What do you think we should ask him?
Those prospects are safe passage to Ecuador's capital Quito, or deportation.
His continued political activism creates diplomatic headaches for Ecuador.
Moreno has warned Assange that he must respect asylum conditions and not to get involved in the affairs of other countries. Due to the fear of being prosecuted, he violated the terms of the bail and sought asylum at Ecuador embassy, Daily Mail reported.
The UK Foreign Office reportedly rejected a request from Quito to grant the whistle-blower diplomatic status. Sweden later dropped the case, but Assange remained ensconced in the embassy because he still faced arrest by British authorities for jumping bail.
If he was deported to Australia, could he still be sent to the US? Assange's legal team has called on United Kingdom and Swedish authorities to end his "deprivation of liberty, respect his physical integrity and freedom of movement, and afford him the right to compensation".
But Professor Rothwell said there were limits in what assurances Mr Assange can be given.