* U.S. manufacturing activity fell in July
* Euro hurt as Greek stock market plunges
* U.S. jobs data on Friday in focus
* Canadian dollar weakest in decade as oil slides (Updates prices, adds comment, background, changes dateline; previous LONDON)
By Karen Brettell
NEW YORK, Aug 3 (Reuters) - The dollar pared gains against the euro on Monday after data showed the pace of growth in the U.S. manufacturing sector slowed in July.
The Institute for Supply Management said its index of national factory activity fell to 52.7 from 53.5 the previous month. The reading was shy of expectations that the pace would remain unchanged at 53.5, according to a Reuters poll of economists. A reading above 50 indicates expansion in the manufacturing sector.
The dollar remained higher on the day, however, as investors awaited jobs data for July that will be released on Friday. A strong jobs report will boost expectations that the Federal Reserve is closer to raising interest rates, which many see as likely to begin in September.
"The dollar rally's back on track," said Win Thin, global head of emerging market strategy at Brown Brothers Harriman & Co in New York. "The Fed is ready to lift-off, if we get a strong reading on jobs, over 200,000, the lift-off is on track."
The dollar last traded against the euro at $1.0974 EUR= after earlier rising as high as $1.0942.
The greenback also gained against the euro as the Greek stock market plunged on its reopening following a five-week shutdown.
"The drop in the Greek stock market has put the euro under slight pressure," said Yujiro Goto, currency strategist at Nomura.
Losses in the euro were capped by data showing euro zone factory activity grew more quickly than previously thought in July.
The Canadian dollar and emerging market currencies weakened as crude oil prices fell.
"The commodities story is having strong repercussions across markets," said Brown Brothers' Thin.
The Canadian dollar fell to its lowest in more than a decade against the greenback. The dollar rose to C$1.3175, its highest since September 2004.