Core inflation in Tokyo stays below BOJ goal, factory output rebounds

* May Tokyo core CPI rises 1.3% yr/yr vs forecast +1.5%

* Index excluding fresh food, fuel rises 1.6% yr/yr

* Factory output rebounds in April on brisk AI demand

* Analysts expect inflation to re-accelerate on energy shock (Adds analyst quotes, factory output in paragraphs 2, 4, 8-9, 12-16)

By Leika Kihara

TOKYO, May 29 (Reuters) - Annual core inflation in Japan's capital stayed below the central bank's 2% target for a fourth straight month in May, data showed on Friday, as fuel and tuition subsidies offset rising raw material costs from the U.S.-Israeli war on Iran.

Separate data showed factory output rebounded in April as brisk AI-driven demand masked weakness in other sectors hit by the Middle East conflict, suggesting the economy was weathering the pain from rising fuel costs at least for now.

The data will be among the factors the Bank of Japan will scrutinise at next month's policy meeting, when markets expect a hike in its short-term policy rate to 1% from 0.75%.

"The April activity data show that Japan's economy is shrugging off the energy cost shock and cement the case for a BOJ rate hike next month," said Marcel Thieliant, head of Asia-Pacific at Capital Economics.

The Tokyo core consumer price index (CPI), which excludes volatile fresh food costs, rose 1.3% in May from a year earlier, slowing from a 1.5% gain in April. It was the sixth straight month of slowdown and fell short of median market expectations for a 1.5% rise.

The slowdown in Tokyo core CPI, viewed as a leading indicator of nationwide price trends, was largely due to the effect of subsidies to curb utility, water bills and tuition.

Analysts expect inflation to re-accelerate in the coming months as surging oil prices and higher import prices from a weak yen keep the BOJ under pressure to raise interest rates.

"Cost-pressure from the Middle East conflict will push up prices not just for energy but a wide range of goods," said Masato Koike, a senior economist at Sompo Institute Plus.

"Government steps could mitigate some of the upward price pressures but not all, thereby pushing real wages back to negative territory," said Koike, who expects a BOJ hike in July.

An index stripping away the effect of fresh food and fuel, which is closely watched by the BOJ as a better gauge of trend inflation, rose 1.6% in May after a 1.9% gain in April.

The BOJ kept interest rates steady in April, but dropped strong signals about the chance of a near-term hike due to mounting inflationary pressures.

The Middle East conflict has complicated the BOJ's decision on the timing and pace of rate hikes, as higher energy costs fuel inflation while simultaneously squeezing an economy heavily dependent on oil imports.

While Japan's economy grew faster than expected in the first quarter on solid exports and consumption, analysts warn momentum will face a severe test as the full force of the energy shock from the Iran war filters through to businesses and consumers.

Separate government data showed on Friday factory output rose 0.8% in April from the previous month, confounding market forecasts for a 0.9% drop.

While shipments of naphtha fell 16.2%, production of industrial and electric machinery rose with chip inspection equipment surging 44.3%, the data showed.

Manufacturers surveyed by the government expect output to rise 5.1% in May before falling 0.4% in June, the data showed.

(Reporting by Leika Kihara; Editing by Thomas Derpinghaus and Sam Holmes)