(Corrects to say estimate was for a fall, not gain, paragraph 2) TOKYO, July 1 (Reuters) - Japan's core consumer prices fell 0.4 percent in May from a year earlier, government data showed on Friday.

The core consumer price index, which includes oil products but excludes fresh food prices, matched economists' median estimate for a 0.4 percent annual fall.

The so-called core-core inflation index, which excludes food and energy prices and is similar to the core index used in the United States, rose 0.6 percent in the year to May.

Core consumer prices in Tokyo, available a month before the nationwide data, fell 0.5 percent in June from a year earlier, versus a 0.5 percent annual fall seen by analysts in a Reuters poll.

(Reporting by Stanley White)