Jan 5 (Reuters) - Canada's main stock index snapped a two-day rising streak and fell on Thursday, tracking weak oil and crude prices, while disappointing U.S. private employment data added to fears about the Federal Reserve keeping rates higher for longer.

At 0935 a.m. ET (1435 GMT), the Toronto Stock Exchange's S&P/TSX composite index was down 110.58 points, or 0.56%, at 19,478.25. (Reporting by Johann M Cherian in Bengaluru; Editing by Shinjini Ganguli)