* Manufacturer sentiment index +2 in March, flat in June * Service sector sentiment +5 in March, +9 in June * Poll points to improvement in BOJ March tankan * Respondents say worst over but recovery moderate By Tetsushi Kajimoto and Sumio Ito TOKYO, March 22 (Reuters) - Japanese big manufacturers turned optimistic about business conditions for the first time in four months, with their sentiment index for March jumping on a strengthening U.S. economy and the yen's retreat from record highs, a Reuters monthly poll showed. The 13 point advance in sentiment was the biggest gain in more than 2-1/2 years, providing more evidence that Japan's economy is recovering from last year's earthquake, flooding in Thailand and appreciation in the yen. But highlighting risks posed by European debt problems and high oil prices, manufacturing confidence was seen only steady in June, with respondents saying that even if the worst is behind them, the recovery would be moderate at best. The service sector mood was positive, albeit unchanged, in March and is expected to edge up another 4 points in June to its the highest reading since December 2007. The Reuters Tankan is highly correlated with the Bank of Japan's quarterly tankan survey and suggests that the next central bank survey, due on April 2, could also show a marked improvement. The BOJ's tankan will help the central bank judge whether the economy is on track for a moderate recovery or if it needs further stimulus. Many market players expect the BOJ to ease policy further in the coming months after it took a more committed stance to beating persistent deflation by setting an inflation goal. The BOJ kept monetary policy on hold last week after easing in February. In the Reuters Tankan, the manufacturers' sentiment index, derived by subtracting the percentage of pessimistic responses from optimistic ones, rose 13 points to plus 2, the biggest monthly gain since June 2009 and is seen flat at plus 2 in three months time. Sectors including automobiles, electronics, steel and textiles saw marked improvements in confidence, although sluggish demand and stubborn price falls remain a concern. "Inventory adjustment for semiconductors is continuing. The worst period is behind us but the recovery is moderate," a machinery maker said. Reuters polled 400 big firms from March 1-16, with 252 responding. The index for non-manufacturers stayed flat at plus 5 and is expected to improve to plus 9 in June, underpinned by sectors such as construction and real estate that could benefit from reconstruction-related demand. The BOJ's last tankan survey in December showed big Japanese manufacturers turned pessimistic in the final quarter of 2011 as the world's No.3 economy suffered a mild contraction due to flooding in Thailand, Europe's debt crisis and the yen's strength. But analysts expect growth to have bounced back in the first quarter of this year. With some progress on Europe's debt problems and brighter signs in the U.S. economy, the yen has traded in a 83-84 range against the dollar recently, far from its record high of 75.31 yen on Oct. 31 when Japan intervened heavily to protect exporters. A string of robust economic data has also strengthened the case for a more self-sustaining U.S. recovery with recent figures showing the number of Americans claiming new jobless benefits at a four-year low and a pick-up in manufacturing activity in the Northeast.