Also, they said, investors showed muted participation awaiting cues from domestic manufacturing PMI (Purchasing Manager's Index) numbers to be released this week.
At the interbank foreign exchange, the local unit opened at 83.72 and slipped further to 83.75 against the American currency, registering a loss of 6 paise from its previous close.
On Friday, the rupee fell 3 paise to settle at 83.69 against the American currency.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.07 % to 100.17.
According to analysts, the dollar strengthened after the US core personal consumption expenditures (PCE) price index for August came in line with market expectations, firming hopes of further interest rate cut by the Federal Reserve.
Brent crude, the international benchmark, advanced 0.71 % to 72.49 in futures trade.
On the domestic equity market front, the Sensex declined 353.49 points or 0.41 % to 85,218.36, while the Nifty fell 86.75 points or 0.33 % to 26,092.20.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Friday as they offloaded shares worth Rs 1,209.10 crore, according to exchange data.
Analysts said a revival of economic activity in China may prompt foreign investors to withdraw from India and other emerging markets and infuse capital in China.
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