It marks a fall from the peak of 7.8 percent through the year to the December quarter last year.
CPI inflation slowed in the June quarter, with the quarterly rise being the lowest since September 2021, Michelle Marquardt, ABS head of price statistics, said in a statement.
"While prices continued to rise for most goods and services, there were some offsetting price falls this quarter including for domestic holiday travel and accommodation and automotive fuel."
Rents were the biggest contributor to the CPI rise in the June quarter, rising by 2.5 percent, the biggest quarterly increase since 1988.
The cost of international travel and accommodation rose by 6.2 percent, largely driven by high demand for travel to Europe during the summer peak season, and food prices by 1.6 percent.
"Rents recorded the strongest quarterly rise since 1988, reflecting low vacancy rates amid a tight rental market. Rental price growth for flats continued to outpace the growth for houses," said Marquardt.
Responding to the data, Treasurer Jim Chalmers said it was promising to see inflation regulated, but high inflation and interest rate rises are continuing to squeeze household budgets.
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