* Rupee off one-month highs as refiners buy dollars * Fed rate decision will be closely watched * Gains in stocks raise hopes of some fresh inflows (Updates to close) By Swati Bhat MUMBAI, Dec 16 (Reuters) - The Indian rupee strengthened on Tuesday, buoyed by broad dollar weakness and later supported by gains in local shares, but was knocked off one-month highs by dollar demand from oil refiners. Dealers said an expected rate cut by the U.S. Federal Reserve would help the rupee gain. The Fed is widely seen cutting its key rate by 50 basis points to 0.5 percent later in the day. The partially convertible rupee closed at 47.92/93 per dollar, 0.3 percent stronger from Monday's close of 48.05/06. It rose to 47.79 in the session, its strongest since Nov. 11. "The rupee rose initially due to the dollar's weakness but then that came off. There was also some dollar demand from state-run banks which could likely be on behalf of oil companies," a senior dealer at a state-run bank said. "There was good two-way interest in the market," he added.

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