* Rupee ends at 53.76/77 per dlr vs 53.91/92 on Monday
* RBI rate cut seen supportive of economic growth
* Rupee seen range-bound; budget, balance of payments key
By Swati Bhat
MUMBAI, Jan 29 (Reuters) - The Indian rupee strengthened to its highest level in a week on Tuesday after the central bank cut interest rates as well as banks' cash reserve ratio, with dollar inflows tied to a sizeable share sale also aiding.
Traders said the central bank's decision to cut the repo rate after nine months indicates a tilt in its policy to support growth, which should help the rupee in the medium term.
Still, India's central bank struck a cautious note on further easing as it waits to see how the government's upcoming budget will aim to bring a bloated fiscal deficit under control.
"The policy was in line with expectations and I expect the rupee to hold in a broad range of 52 to 55 over the next one to two months. The budget would be the next big thing," said Ashtosh Raina, head of foreign exchange trading at HDFC Bank.
"There were good dollar inflows seen today, which helped offset the month-end dollar demand from oilers."
The partially convertible rupee closed at 53.76/77 per dollar, stronger than its Monday close of 53.91/92. The rupee rose to a high of 53.5475 during the session, its strongest since Jan. 22.
The rupee was also supported by dollar inflows that traders attributed to a qualified institutional placement of up to $1 billion by Axis Bank Ltd.
Traders also saw intermittent dollar buying from oil firms, the biggest buyers of the greenback in the domestic currency market, whose demand tends to peak at the end of each month when most are required to make import payments.
Standard Chartered Bank said in a note the fundamental backdrop for the rupee remains mixed, with the currency likely to be range-bound but volatile until there are discernible signs of sustained improvement in the balance of payments.
In the offshore non-deliverable forwards, the one-month contract was at 54.04, while the three-month was at 54.60.
In the currency futures market, the most-traded near-month dollar/rupee contracts on the National Stock Exchange, the MCX-SX and the United Stock Exchange all closed at around 54.06 with total traded volume of $5.12 billion. (Editing by Prateek Chatterjee)
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