The rupee depreciated 4 paise to 83.36 against the US dollar in the morning session on Thursday, tracking the strength of the American currency in the overseas market and muted trend in domestic equities.
Forex traders said rupee is trading in a narrow range as the support from easing crude oil prices was negated by strong dollar demand from importers.
At the interbank foreign exchange, the rupee opened at 83.36 against the dollar, registering a fall of 4 paise over its previous close.
On Wednesday, the rupee appreciated by 5 paise and settled at 83.32 against the greenback, as flows resumed and RBI protected the key 83.40 level.
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"Brent oil fell to a low of USD 74.63 per barrel which is a six-month low on US output being at record highs even though inventories fell. This should be quite positive for the rupee," said Anil Kumar Bhansali, Head of Treasury and Executive Director Finrex Treasury Advisors LLP.
Brent crude futures, the global oil benchmark, was trading higher by 0.50 per cent to USD 74.67 per barrel.
Bhansali further noted that the rupee is expected to remain in a narrow range of 83.30 to 83.40 for the whole day as USD inflows are bought by bids/outflows from oil and importers.
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Investors are also awaiting cues from the RBI's monetary policy meeting. The Monetary Policy Committee meeting commenced on Tuesday with a decision due on Friday.
The Reserve Bank is likely to maintain the status quo on the short-term interest rate in its monetary policy review.
RBI Governor Shaktikanta Das-headed Monetary Policy Committee (MPC) is scheduled to begin its three-day deliberations on December 6. Das would unveil the decision of the six-member MPC on December 8.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.03 per cent higher at 104.17.
In the domestic equity market, the 30-share BSE Sensex was trading 250.76 points or 0.36 per cent lower at 69,402.97 points. The broader NSE Nifty fell 63.15 points or 0.3 per cent to 20,874.55 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Wednesday as they offloaded shares worth Rs 79.88 crore, according to exchange data.