By Leika Kihara

TOKYO (Reuters) - Core consumer prices in Japan's capital rose 2.1% in June from a year earlier, data showed on Friday, accelerating from the previous month as rising fuel bills and the boost to import costs from a weak yen weighed on households.

The data highlights the challenge the Bank of Japan (BOJ) faces in timing its next interest rate hike, as cost pressures from the weak yen keep inflation above its 2% target - but also hurt consumption.

The increase in Tokyo's core consumer price index (CPI), a leading indicator of nationwide figures, compared with a median market forecast for a 2.0% gain and followed a 1.9% rise in May.

A separate index that excludes the effects of fresh food and fuel costs, closely watched by the BOJ as a broader price trend indicator, rose 1.8% in June after a 1.7% gain in May.

Japan's economy shrank an annualised 1.8% in the first quarter as companies and households reduced spending, casting doubt on the central bank's view of a moderate recovery.

While analysts expect growth to rebound in the current quarter, a weak yen is weighing on household sentiment by pushing up the cost of imports for fuel and food.

The BOJ ended eight years of negative interest rates and other remnants of its radical monetary stimulus in March as it judged that sustained achievement of its 2% inflation target has come into sight.

BOJ Governor Kazuo Ueda has said the central bank will raise interest rates from current near-zero levels if underlying inflation, which takes into account CPI and broader price gauges, accelerates toward 2% as it currently projects.

The central bank expects rising wages to push up service inflation and keep inflation durably around 2%, a condition it set as a prerequisite to further phase out monetary stimulus.

(Reporting by Leika Kihara; Editing by Sam Holmes)