* TSX falls 15.83 points, or 0.13 percent, at 12,593.97 * Seven of 10 main sectors decline * CP Rail sheds 2.8 percent after activist investor move, downgrade * Barrick declines after project delay, bullion price fall By John Tilak TORONTO, June 4 (Reuters) - Canada's main stock index fell on Tuesday to a two-week low, hurt by declines in Canadian Pacific Railway Ltd and Barrick Gold Corp as well as concerns that the U.S. Federal Reserve might taper its stimulus program. RBC Capital Markets cut its rating on CP Rail, a day after activist investor Pershing Square Capital Management said it would sell nearly one-third of its roughly 14 percent stake in the company. CP shares tumbled 2.8 percent. The market was further weakened as declines in the price of bullion, which fell on concerns about demand in India, pulled shares of gold producers lower. But rising oil prices, fueled by rumors that South Korea would create new incentives for refiners to import crude, boosted energy companies and kept losses in check. Speculation that the U.S. central bank might taper off its bond buying is the single biggest source of market volatility, said Elvis Picardo, strategist and vice president of research at Global Securities in Vancouver. "The Fed is even now talking about taking the punch bowl away," he added. "It's going to be quite a challenge for the market to grapple with that." "We're seeing increased sensitivity to this sort of talk in recent weeks, and we suspect that the volatility is going to continue." The Toronto Stock Exchange's S&P/TSX composite index closed down 15.83 points, or 0.13 percent, at 12,593.97, falling earlier to 12,568.94, its lowest since May 17. Canadian stocks have sharply underperformed their U.S. peers so far this year. The sentiment for Canadian equities is "subdued," said Stan Wong, vice president and portfolio manager at Macquarie Private Wealth. "The story in Canada surrounds the fact that the housing market is a little bit weaker and commodity prices are falling," he added. "And that's going to continue to spell trouble for the TSX." Seven of the 10 main sectors on the Canadian benchmark index were in the red on Tuesday. Financials, the index's most heavily weighted sector, fell 0.1 percent. The gold sector, down about 33 percent this year, shed 1.4 percent. Barrick Gold Corp lost 1.7 percent to trade at C$21.58, and Goldcorp Inc fell 0.8 percent to C$30.42. Barrick said late on Monday it would delay the startup of its Pascua-Lama gold mine in Chile and Argentina past late 2014 and that as a result, the project would probably exceed its current budget of up to $8.5 billion. Meanwhile, shares in Rogers Communications gave back 0.7 percent to trade at C$46.45, a day after Canada's main industry watchdog said that consumers will be able to cancel their cellphone contracts after two years without penalty, instead of the three years that is the current industry standard. In other company news, Canada blocked Telus Corp's application to assume struggling upstart Mobilicity's wireless spectrum licenses. Telus shares were up 0.1 percent. But energy shares climbed 0.5 percent on higher crude oil prices. Suncor Energy Inc, Canada's largest energy company, gained 1.4 percent to C$31.78 and had the biggest positive influence on the market.