The trio, named by Australia's left-leaning Greens party as Markus Jerewon, Yuvensius Goo and Rofinus Yanggam, reportedly scaled the mission's walls to get inside.
"They are simply calling for independent journalists to be granted access to the region and for West Papuan political prisoners to be released," said Greens Senator Richard Di Natale, chair of a parliamentary Friends of West Papua group.
"They are not seeking independence."
Australia's foreign office said "three individuals from Indonesia's Papua provinces delivered a protest letter at the Australian Consulate-General in Bali this morning to Australia's Consul-General," making no mention of their method of arrival.
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Australian Associated Press said the men were persuaded to move on despite earlier saying they were seeking refuge and feared for their safety if forced to leave the embassy.
The incident came ahead of Australian Prime Minister Tony Abbott's arrival in Bali for the Asia Pacific Economic Cooperation leaders' summit which will be held tomorrow.
According to a handwritten letter from the Alliance of Papua Students trio, cited by AAP, the men demanded that Abbott, Japan's Prime Minister Shinzo Abe and US Secretary of State John Kerry pressure Indonesia on Papuan rights.
"These political prisoners committed no crime. They are explicitly committed to non-violence. The Indonesian government arrested and jailed them for discussing their political human rights beliefs."
The men also called for the international press to be allowed into Papua, where armed militants have for decades fought an insurgency on behalf of the mostly ethnic Melanesian population in Papua.
Indonesian security forces have repeatedly faced allegations of torturing political activists in the restive province.
The men ended their letter saying "we seek refuge and plead for our safety", but AAP said they were convinced to end their protest and vacate the embassy.