Their latest figures showed the overall rate for July was 5.8%-down from last month but the 22nd in a row it has been over 5%.
Inflation is high because of an increase in the cost of mortgage interest repayments, rents, electricity, gas and solid fuels.
These increases were partially offset by a reduction in prices for home-heating oil, the CSO said.
However, home-heating oil prices have started to rise again, with the cost of 1,000 litres of the fuel back over €1,000.
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