The claim was made by Labor communications spokesman Jason Clare on the ABC's Radio National Breakfast programme on 13 June.
When asked about the source, the ABC's Fact Check unit says it was referred to Labor's broadband policy document for the upcoming 2 July election by a spokesman for Clare.
The spokesman said that Akamai's state of the internet quarterly reports were the basis of the claim.
Akamai, a global content delivery and network services company, issues reports on Internet connectivity and security. Its Q4 2015 report is the latest available for connectivity. The Q1 2016 report on security is out.
A number of experts contacted by Fact Check said that Akamai provided a reasonable indication of Internet activity, given the size of its content delivery networks.
Fact Check also contacted David Belson, the editor of the Akamai report, who wrote a blog post earlier this year, explaining the metrics used to obtain data published in the report.
The Fact Check unit concluded: "The (Akamai) reports show Australia's average peak connection speed of 30.1 megabits per second ranked 30th in the world in the quarter ending in September 2013, the month the Coalition took office.
"The most recent report available at the time the claim was made shows Australia's average peak connection speed of 39.3 mbps ranked 60th in the world in the quarter ending in December 2015.
"Experts consulted by Fact Check said the Coalition contributed to Australia's drop in rankings for several reasons, including its policy of rolling out fibre to the node technology rather than fibre to the premises."