WASHINGTON, July 16 (Reuters) - U.S. import prices were unchanged in June as lower prices for energy products offset a rebound in the cost of food, the Bureau of Labor Statistics said on Tuesday.

The flat reading in import prices followed a 0.2% drop in May. Economists polled by Reuters had expected import prices, which exclude tariffs, to dip 0.1%.

In the 12 months through June, import prices increased 1.6%. That followed a 1.4% advance in May.

Moderate import prices supported views that inflation was on a downward path and could provide the Federal Reserve room to cut interest rates in September.

Government data last week showed consumer prices fell in June for the first time in four years. Producer prices rose last month, but details of the reports were much more benign.

Imported fuel prices dropped 1.0% after rising 0.4% in May. Crude petroleum and natural gas prices both declined. The cost of imported food increased 0.7% after dropping 1.6% in May.

Prices for imported capital goods were unchanged. That followed a 0.2% fall in May. The cost of motor vehicles, parts and engines edged up 0.1%. Imported consumer goods prices slipped 0.1%.

Excluding fuels and food, import prices were unchanged. These so-called core import prices dipped 0.1% in May.

Core import prices rose 0.6% year-on-year in June. They are being kept in check by the dollar strength against the currencies of the United States' main trade partners this year as the Federal Reserve has kept interest rates elevated.

The report also showed that export prices fell 0.5% in June after declining 0.7% in May. In the 12 months through June, export prices rose 0.7% after gaining 0.5% in June. (Reporting By Lucia Mutikani; Editing by Sharon Singleton)