"Our expectations are moderate and hopeful", Kristinn Hrafnsson told reporters before the start of the hearing.
Earlier on Monday, Assange arrived for his extradition hearing in London clean shaved .
The hearing is set to determine the agenda of the future hearings for the WikiLeaks founder's potential extradition to the United States. Earlier this month, a judge ruled that Assange had to attend hearings in person while he had been previously allowed to teleconference from prison due to ill health.
The Australian publisher is currently serving a 50-week sentence in London's Belmarsh prison over violating his bail conditions. In the United States, he is facing espionage charges over his work with WikiLeaks that published a large number of leaked classified documents.
Washington has requested the extradition of the whistleblower. The US initially charged Assange with conspiring to carry out a computer offense. However, the US Justice Department subsequently extended the charges so the whistleblower may now face up to 175 years in prison.
Though the UK authorities have said London would not extradite Assange to a country where he faced death penalty, the activist has repeatedly said he feared he might be put on a death row in the United States.