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At 9.04 a.m. local time, the rupee was at 53.72/73 to the dollar against its previous close of 54.30/31. It rose to a high of 53.66, its highest since May 15.
The market is awaiting the central bank's rate decision at 0530 GMT, with any rate cut likely to lead to a further rally in the rupee.
Indian government bond yields also fell on hopes of fiscal consolidation and ahead of the rate decision.
The 10-year yield was down 6 basis points at 8.12 percent.