Representatives of the Wikileaks founder submitted evidence to Westminster Magistrates’ Court claiming that American agencies had expressed interest in testing nappies discarded when Mr Assange’s partner and children visited him at the Ecuadorian embassy.
District Judge Vanessa Baraitser found that, even if the allegation were true, there was no reason to believe US agencies meant to harm his young family.
She referred to the claim while rejecting the bid to anonymise Mr Assange’s partner, who the court heard wishes to live “quietly” with her young children away from publicity.
Following a submission by the Press Association news agency to the court, Judge Baraitser ruled that the woman’s right to a private family life was outweighed by the need for open justice.
But the judge delayed making the woman’s identity public until 4pm on 14 April, pending a possible judicial review at the High Court.
The 48-year-old is being held on remand at HMP Belmarsh, in south-east London, ahead of an extradition hearing on 18 May.
During the virtual hearing, the judge also rejected a bid to delay the hearing because of the coronavirus crisis.
Mr Assange’s barrister, Edward Fitzgerald QC, said there were “insuperable” difficulties preparing his case because of the pandemic, and requested an adjournment until September.
He told the court that he had not been able to see Mr Assange in jail and could see “no viable” way his client could be present in court to hear witnesses.
On Mr Assange’s mental state, he told the judge: “There are difficulties of the pandemic with the defendant himself. You are aware … he has well documented problems of clinical depression.”
Mr Assange’s treatment was on hold during the lockdown and he had been unable to see his family.
Mr Fitzgerald said: “In those circumstances, in his vulnerable condition, to force him to enter a full evidential hearing in May, we respectfully submit it would be unjust. We respectfully submit it would be oppressive.”
He stressed it was an “exceptional circumstance”, adding: “This is not a case where second best will do, where we should just try to muddle through. The difficulties are insuperable in the current crisis.”
Ruling against him, Judge Baraitser said the extradition hearing was still five weeks away and it was expected courts would resume in a fortnight despite the continuing lockdown.
She added: “I cannot assume the courts will not be operating normally by then.
“Mr Assange is in custody and there is some urgency of this case being heard to its conclusion.”
If there was a need for a third and final hearing after the hearing on 18 May, it will be held in July.
Mr Assange is fighting extradition to the US, where he would face 17 charges under the Espionage Act and conspiracy to commit computer intrusion, over the publication of hundreds of thousands of classified documents in 2010 and 2011.
He has been held in custody since being arrested at the Ecuadorian embassy in London almost exactly a year ago.
He sought asylum there in 2012 while wanted under a European Arrest Warrant for interview in a Swedish rape investigation which has since been dropped.
Additional reporting by PA