On a visit to Washington, Bishop praised cooperation with Washington and reserved harsh words for Snowden, whose revelations led Indonesia to halt work with Australia to stem people-smuggling, a key priority for new conservative Prime Minister Tony Abbott.
Shortly before a meeting with US Vice President Joe Biden, Bishop said Snowden "continues to shamefully betray his nation while skulking in Russia.
"This represents unprecedented treachery; he is no hero," he added, in a speech at the Centre for Strategic and International Studies.
Reports based on Snowden's leaks said that Australia, which works closely with the United States, tried to bug the phones of Indonesian President Susilo Bambang Yudhoyono, his wife and members of his inner circle in 2009.
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Indonesia protested by recalling its ambassador and suspending military and immigration cooperation. More recently, Indonesia responded furiously as Australia nonetheless entered Indonesian waters in search of would-be refugees, incursions that led to an apology from Canberra.
He fled to Hong Kong and then to Russia, which granted him asylum for a year.
Snowden has strongly denied allegations of betraying the United States, saying that he has not cooperated with foreign agencies and wanted to expose wrongdoing as he had no means to air concerns internally.
Snowden, described by his Russian lawyer as fearing for his life, has said that he is working with journalists who exercise discretion in deciding which revelations to publish.
Faced with an uproar, Obama on Friday curtailed the reach of the National Security Agency but has said that Snowden's disclosures would hurt the United States for years.