This followed an increase of 0.7pc in the first quarter.
The CSO said the second-quarter increase was mainly driven by an increase in the industry sector.
The GDP figure is down 1.4pc on the same quarter in 2023, indicating the economy is still marginally smaller than it was this time last year.
However, being the tax base for many American multinationals leads to huge swings between growth and decline in GDP.
Enda Behan, a statistician with the CSO, said: “GDP is estimated to have expanded by 1.2pc in April, May and June in volume terms when compared with Q1 2024.
“This was driven by an increase in the multinational-dominated sector of industry in Q2.
“After combining this preliminary estimate for Q2 with the estimate for Q1 from the quarterly national accounts, GDP is estimated to have contracted in the first half of 2024 by 3.1pc when compared with H1 2023.”
Irish GDP fell by 3.2pc last year, mainly as a result of a decline in export activity by the pharma sector in the aftermath of Covid.
Most commentators believe this was not an accurate depiction of how the underlying economy performed in 2023, however.
Headline GDP tends to distort the performance of the domestic economy. Modified domestic demand, which gives a more realistic picture, expanded by 0.5pc last year, although even this indicator may have underestimated domestic activity in 2023.
The Department of Finance has forecast GDP will increase by 2.6pc this year and by 3.9pc next year, according to estimates it published with the stability programme update last April.
Its forecast for modified domestic demand was for an increase of 1.9pc this year, and 2.3pc next year. Another measure, GNI, was forecasted to grow by 2pc this year.
The Economic and Social Research Institute has estimated modified domestic demand will grow by 2.3pc this year and by 2.5pc next year. It expects GDP to grow by 2.5pc this year.
The European Commission has predicted a GDP growth rate of 1.2pc for Ireland this year.
In its spring economic forecast, published in May, it forecast GDP growth of 3.pc for 2025. Its predictions for modified domestic demand were up 1.7pc this year and up 2.4pc next year.