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Yes it can but only to a limited extent. In India and I think in most countries the central bank owned by the gevernment controls the interest range which could be +-1 or2% by all powerful CRR. Every commercial bank has to keep a % of the banks assets with the central bank. By changing this deposit as % of total assets the central bank contols the interest rate range.
If the bank needs more money from the market in the short or long term it could increase the rate of fixed deposit interest for short (could be as short as15 days to3months) or long term(normally maximum of3-5years)comapred to other banks . But the rates have to be within the range as dictated by the government owned central bank.
