Assange is accused of sexual assault by two women he met last year during a visit to Stockholm.
At the start of the hearing, Assange's lawyer Geoffrey Robertson argued that closed-door hearings would be "a flagrant denial of justice ... blatantly unfair, not only by British standards but by European standards and indeed by international standards."
Swedish rape trials are customarily held in secret.
A British lawyer representing Sweden countered that Swedish trials were based on the principle that everyone deserves "a fair and public hearing." She said that in cases where evidence is heard in private it will often be published after the trial and recited in the judgment.
Assange's lawyers also argue that sending him to Sweden could land him in Guantanamo Bay or on death row in the U.S.
Assange claims he is being prosecuted for political reasons because of his website's release of secret documents.
The Associated Press contributed to this report.