June 28 (Reuters) - Spain's European-Union harmonised inflation rate fell to 3.5% in the 12 months through June, from 3.8% in the period through May, preliminary data from the National Statistics Institute (INE) showed on Friday.

The lower inflation is mostly due to a decrease in fuel prices, compared to an increase in the same period last year, and a slower increase in food prices, INE said.

The 12-month harmonised inflation rate was slightly faster than the 3.4% average expectation from analysts polled by Reuters.

Core inflation, which strips out volatile fresh food and energy prices, stood at 3.0% in the 12 months through May, the same pace as a month earlier, INE said.

Spain's government passed an inflation relief package worth nearly 3 billion euros ($3.21 billion) on Tuesday, including measures such as a lower income tax for minimum wage workers and an extension of zero value-added tax on basic food items.

The Spanish 12-month national consumer price index rose 3.4% in May, down from 3.6% in April. (Reporting by Joao Manuel Mauricio in Gdansk, editing by Inti Landauro and Sharon Singleton)