* Exporter dlr conversions help rupee gain

* Stocks at 3-wk low amid foreign buying

* Rising interest rate, rupee concerns trim volume

COLOMBO, July 4 (Reuters) - The Sri Lankan rupee edged up on Wednesday on exporter demand for the currency, dealers said, while concern over rising interest rates drove the share market down in thin trade.

The rupee closed at 133.70/80 to the dollar, slightly firmer than Monday's close of 133.80/90.

Both stock and money markets were closed on Tuesday for a Buddhist holiday.

The rupee hit another in a series of record lows on June 28, at 134.30.

"The rupee appreciated a bit due to exporter dollar conversions," said a currency dealer on condition of anonymity. "The rupee may rise further as imports will decline due to continuously rising interest rates."

Yields in 91-, 182- and 364-day T-bills edged up to three-year highs at a weekly auction.

Sri Lanka's central bank has taken several stringent policy measures this year aimed at cutting imports, including raising policy rates twice to two-year highs and restricting credit growth, though a prolonged drought has increased oil imports for thermal power.

Dealers expect pressure on the rupee to ease if the central bank stops aggressive dollar buying. The central bank, which was a big buyer of dollars last month, told Reuters on Friday that Sri Lanka had met all June-end IMF targets for the last tranche of a $2.6 billion loan.

The rupee has lost 17.5 percent of its value since November, when the government allowed a 3 percent devaluation. The sharp fall drove the annual inflation rate to a 41-month high in June, data showed on Friday.

Concern over inflation and rising interest rates extended the Colombo Stock Exchange's main index fall to a fourth straight session with the index losing 0.13 percent or 6.35 points to 4,946.58, its lowest since June 14.

Turnover was 377.9 million rupees ($2.83 million), well below this year's daily average turnover of 969.6 million rupees.

Foreign investors were net buyers of 164.1 million rupees worth of shares on Wednesday, extending the net inflow this year to 23.34 billion rupees. ($1 = 133.7500 Sri Lanka rupees) (Reporting by Ranga Sirilal and Shihar Aneez; Editing by Robert Birsel)