* April seasonal importer demand diminishes * Bourse slips; high interest rates, rupee weigh (Reuters) - Sri Lanka's rupee closed marginally firmer on Tuesday on exporter dollar conversions and inflows from worker remittances, and as April seasonal importer demand declined to ease depreciation pressure, dealers said. The rupee inched up to close at 129.80/130.00 a dollar from Monday's close of 130.00/130.10. It hit a record low of 131.60 on Mar. 19, mainly due to importer demand for greenbacks for the upcoming April festive season. Dealers see the rupee gaining now that pre-festival import demand is declining, and dollar supplies are growing as exporters convert to pay holiday bonuses and expatriate workers send home money for relatives to spend during the festival. The rupee has fallen 12 percent since the central bank stopped defending a specific price on Feb. 9. The stock market meanwhile slipped in thin volume as many investors remained cautious of rising interest rates, the rupee's volatility and an expected fall in overall profits. The island nation's main share index edged down 0.11 percent or 5.96 points to 5,425.00. The day's turnover was 578.6 million Sri Lanka rupees ($4.45 million), well below last year's daily average of 2.3 billion. Volume was 30.7 million. Last year's daily average was a record 102.7 million. Foreign investors were net buyers of 25.4 million on Tuesday, extending the net foreign inflow so far this year to 20.1 billion Sri Lanka rupees ($154.56 million) worth of shares so far this year, after a net outflow of 19.1 billion last year. The Colombo bourse is one of the worst performers this year among Asian markets, with a 10.7 percent loss. ($1 = 130.0500 Sri Lanka rupees) (Reporting by Ranga Sirilal and Shihar Aneez; Editing by Bryson Hull)

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