According to Twitter's Transparency Report, Australian authorities asked Twitter for information on 58 users in the first six months of 2013, compared with fewer than 10 in the second half of 2012.
Only the United States and Japanese governments sought information about more accounts according to the report, first launched in July 2012.
The news comes as Twitter moves to block online bullying, through a new 'anti abuse' button announced this week.
No further information was available on the specifics of these requests or who they pertained to, though users are usually notified if their information is being requested.
Australia’s total of 58 users investigated was behind the US (1319 users in 902 requests) and Japan (103 users in 87 requests), with Brazil (44 users in 22 requests), France (35 users in 18 requests) and the UK (29 users in 26 requests).
25% of Australia's requests were successful, meaning some or all of the requested information was provided by Twitter. This compares to Brazil's 32% success rate, Japan with 16%, the UK with 15% and France with 11%. 67% of United States requests produced some or all of the information.
Twitter said 1157 requests in total came from 26 different governments between January and June, 2013, including Canada, Germany, the Netherlands and Turkey, while more than 900 of the requests came from the US, accounting for 78% of the total number. None came from New Zealand.
''Twitter remains steadfastly committed to being transparent about requests we've received and the resulting actions we've taken,'' said Jeremy Kessel, Twitter's manager of legal policy, in a blog post.
"We believe the open exchange of information can have a positive global impact."