By Fergal Smith

TORONTO, July 2 (Reuters) - The Canadian dollar strengthened against its U.S. counterpart on Wednesday as investors weighed a potential easing of global trade tensions and clues on the state of the U.S. labor market.

The loonie CAD= was trading 0.4% higher at 1.3595 per U.S. dollar, or 73.56 U.S. cents, stopping just short of the two-week high it touched on Tuesday at 1.3588.

U.S. private payrolls fell for the first time in more than two years in June as economic uncertainty hampered hiring, the ADP National Employment Report showed.

"The weakness of the ADP, it increases the downside risks to tomorrow's jobs report," said Marc Chandler, chief market strategist at Bannockburn Global Forex LLC.

Economists expect data on Thursday to show U.S. non-farm payrolls increasing by 110,000 in June.

U.S. President Donald Trump said the United States said it will place a lower-than-promised 20% tariff on many Vietnamese exports.

"The move is clearly fostering market optimism for further trade deals with major trading partners in the coming days," said Kevin Ford, FX & macro strategist at Convera.

The U.S. dollar .DXY gave back some earlier gains against a basket of major currencies, while the price of oil settled 3.1% higher at $67.45 a barrel as Iran suspended cooperation with the U.N. nuclear watchdog. Oil is one of Canada's major exports.

The downturn in Canada's manufacturing sector deepened in June as U.S. tariffs undercut demand. The S&P Global Canada Manufacturing PMI edged down to 45.6 in June from 46.1 in May.

Canadian bond yields moved higher across a steeper curve as the market reopened following the Canada Day holiday on Tuesday.

The 10-year CA10YT=RR was up 9.2 basis points at 3.366%, after earlier touching its highest level since June 17 at 3.380%. U.S. Treasury yields also rose, underpinned by fiscal concerns.

(Reporting by Fergal Smith; Editing by Alistair Bell)

((fergal.smith@thomsonreuters.com; +1 647 480 7446;))