If the court rules in Assange's favour, allowing him to leave the embassy in the British capital without fear of arrest, it would be the first time that he has stepped outside embassy grounds since seeking asylum there in June 2012.
Assange entered the Ecuadoran embassy to dodge a European arrest warrant and extradition to Sweden over a 2010 probe in the Scandinavian country into rape and sexual assault allegations.
Assange's lawyer Mark Summers told a London court last week that the warrant had "lost its purpose and its function".
He said Assange had been living in conditions "akin to imprisonment" and his "psychological health" has deteriorated and was "in serious peril".
The court heard that the 46-year-old was suffering from a bad tooth, a frozen shoulder and depression.
But prosecutor Aaron Watkins called Assange's court bid "absurd".
Assange has refused to leave the embassy, claiming he fears being extradited to the United States over WikiLeaks' publication of secret US military documents and diplomatic cables in 2010.
US Attorney General Jeff Sessions last year said his arrest was a "priority".
Assange only very rarely emerges on the balcony of the embassy building, citing concerns for his personal safety, but frequently takes part in media conferences and campaigns via video link.
But London swiftly rejected the move.
"Ecuador knows that the way to resolve this issue is for Julian Assange to leave the embassy to face justice," the British government said.
Assange has strained the patience of his hosts during his long stay.
He was publicly reprimanded for interfering in the 2016 US election after publishing hacked emails from the campaign team of Democrat Hillary Clinton.
Moreno was forced to respond to complaints from the Spanish government.
Moreno, in office since 2017, said last month Assange was an "inherited problem" that had created "more than a nuisance" for his government.
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