Besides, the dollar also strengthened against other currencies such as the euro in the overseas market following disappointing US jobs growth figures, putting further pressure on the rupee, dealers said.
The domestic currency has fallen past the 56-level against the dollar after June 29.
The rupee opened the day weaker, at Rs 55.90 a dollar, but recovered temporarily to 55.82 before slipping again to breach the 56-mark at 56.01 at 1130 hrs, down by 59 paise over the previous close of Rs 55.42 on Friday.
The rupee had lost 45 paise in the last session.
Meanwhile, the BSE benchmark Sensex was down 65.77 points, or 0.38 per cent at 17,455.35.
