* Inflation confirmed at 2.4 percent in June y/y
* May imports unchanged y/y, exports weaken from April
BRUSSELS, July 16 (Reuters) - A sharp fall in energy prices helped cool consumer prices in the euro zone in June and gave the European Central Bank space to cut interest rates this month to try to revive the economy, but stagnant imports highlighted the depth of the downturn.
Consumer inflation in the 17-nation euro zone was 2.4 percent in June on annual basis, the EU's statistics office Eurostat said on Monday, confirming its earlier reading in the month and holding steady at a 16-month low.
Spelling out in detail the factors behind the inflation trend, Eurostat said energy prices fell 1.7 percent in the month from May and consumer prices dipped across 10 of the bloc's members from April. Food, alcohol and tobacco prices rose 0.3 percent.
The ECB cut rates to a record low of 0.75 percent earlier this month and President Mario Draghi said last week that inflation in the euro zone is slowing faster than forecast.
Draghi also said inflation is heading towards the ECB's target of close to, but below 2 percent.
The ECB's rate cut should make it cheaper for households and firms to borrow, but it may take more than that to kick-start the euro zone's depressed economy as its debt crisis eats away at businesses' confidence to invest and hire new staff.
In a sign of the weak economy, euro zone imports in May showed no growth compared to the same month a year ago, Eurostat said in separately released data. Adjusted for seasonal swings, imports notched up their third straight month of falls and slipped 0.9 percent in May compared to April.
With a record 17 million people jobless in the euro zone and many other workers facing frozen or reduced salaries, consumers are not in a position to boost the bloc's economy.
The euro zone is increasingly reliant on its exports sector for any hope of a recovery later this year, and euro zone exports did rise 6 percent in May on annual basis.
However, on a monthly basis, adjusted for seasonal factors, exports rose just 0.3 percent, not enough to make up for a 1.4 percent fall in April as China's economy slows and the United States struggles to expand at anything more than a modest pace.