* Canadian dollar at C$1.2980, or 77.04 U.S. cents
* Price of U.S. oil falls 0.3 percent
* Bond prices higher across the yield curve
TORONTO, June 5 (Reuters) - The Canadian dollar weakened against its U.S. counterpart on Tuesday as oil prices fell and U.S. President Donald Trump mulled moving toward bilateral discussions on NAFTA.
Trump is considering a shift in the effort to revamp the North American Free Trade Agreement to separate talks with Canada and Mexico, White House economic adviser Larry Kudlow said. sends about 75 percent of its exports to the United States so its economy could be hurt if a deal on NAFTA is not reached.
The price of oil, one of Canada's major exports, fell following a report that the U.S. government had asked Saudi Arabia and other major exporters to increase oil output. crude CLc1 prices were down 0.3 percent at $64.53 a barrel.
At 9:13 a.m. EDT (1313 GMT), the Canadian dollar CAD=D4 was trading 0.4 percent lower at C$1.2980 to the greenback, or 77.04 U.S. cents. The currency traded in a range of C$1.2915 to C$1.3007.
Canadian labor productivity fell by 0.3 percent in the first quarter, reflecting a deceleration in business output from the previous quarter, while hours worked accelerated, Statistics Canada said.
Canadian government bond prices were higher across the yield curve in sympathy with U.S. Treasuries and German Bunds. The two-year CA2YT=RR rose 5 Canadian cents to yield 1.909 percent and the 10-year CA10YT=RR climbed 34 Canadian cents to yield 2.238 percent.
Canada's trade report for April is due on Wednesday and the May employment report is due on Friday.