The domestic currency in Tuesday's trade opened a tad lower at 68.56 versus the previous day's close of 68.54 per US dollar. Rupee's weakness comes amid sluggishness in global emerging market currencies.
Dollar has been trading lower after Jerome Powell raised hopes of an interest rate cut by the Federal Reserve later in the month.
Meanwhile, oil prices also headed southwards for the second consecutive day after China reported slowest economic growth for the quarter in nearly 3 decades time. Also, as more of production units in the US Gulf re-started their operations, oil prices declined.
The yields on the benchmark 10-year government bonds were down 0.5 percent to 6.40% from its previous close of 6.43%. Bond yields and prices move in opposite directions.