The broader NSE Nifty ended 1.85 percent higher at 10,386.60, while the benchmark BSE Sensex closed 1.63 percent higher at 34,442.05.
Still, the Nifty registered its worst month since February 2016, down 6.7 percent. The Sensex ended October 4.9 percent lower.
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Housing finance companies were relieved after the government clarified its stance on the central bank, an analyst said, adding that the stocks may have been helped after a housing finance company said it had raised capital.
Indiabulls Housing Finance Ltd ended 8.5 percent higher, while Housing Development Finance Corp gained nearly six percent.
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