Earlier this month the European Central Bank (ECB) introduced fresh measures designed to boost the eurozone, including a "below-zero" interest rate and cheap, long-term bank loans.
ECB president Mario Draghi has referred to inflation below 1% as being in "the danger zone".
The bank wants inflation to be near 2%.
Flash estimates from the EU statistics office, Eurostat, show that the service industry was the only sector to report significant price growth, with a rise of 1.3%, but food, alcohol & tobacco prices were down 0.2%, and industrial goods remained unchanged.
Separate figures from the eurozone showed that retail sales in Greece enjoyed their strongest annual rise in more than two years in April, up 7.3% compared with the year before.
In Germany, retail sales in May were up 1.9% compared with the year before, but down 0.6% compared with April's figures.
Earlier this month, the ECB became the first major central bank to introduce negative interest rates, in an effort to get money moving into the stagnant eurozone economy.
There had been concerns that the eurozone could slip into deflation, raising fears that consumers might spend even less because they would expect prices to fall in future months.
Howard Archer, an economist at IHS Global, said there may be "some relief" within the ECB that eurozone inflation did not weaken further in June.
"Nevertheless, the ECB will likely have been hoping that inflation would actually edge a little higher in June following a marked move back up in German inflation," he added.
The rate of inflation in the eurozone remained at 0.5% in June, marking the ninth consecutive month of below-target growth in the 18 member states.