(Adds European stocks, graphics; updates prices throughout)
* MSCI Asia-Pacific index falls 1.1 pct, Nikkei at new 27-yr highs
* Spreadbetters see European stocks to open lower Canadian dollar stands near 4-mth high, euro sags on Italy woes
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVhCrude oil prices elevated near 4-yr peaks
By Shinichi Saoshiro
TOKYO, Oct 2 (Reuters) - Asian stocks fell on Tuesday as the lift from an agreement that saved the North American free trade deal faded, with cautious views on the global economy curbing risk sentiment.
MSCI's broadest index of Asia-Pacific shares outside Japan fell 1.3 percent after a steady start.
Australian stocks lost 0.7 percent and South Korea's KOSPI fell 0.9 percent.
Bucking the overall trend, Japan's Nikkei added 0.1 percent, after rising as much as 0.8 percent to a new 27-year intra-day high of 24,448.07.
Spreadbetters expected a weaker tone in European equities, forecasting a lower open for Britain's FTSE, Germany's DAX and France's CAC.
China's financial markets are closed for the week of Oct. 1-5 for national holidays.
Hong Kong's Hang Seng, which did not trade on Monday due to a holiday, dropped 1.9 percent in reaction to signs of weakness in the Chinese manufacturing sector shown in purchasing managers' index (PMI) numbers released on Sunday.
"While news that the U.S. and Canada had struck a new NAFTA trade deal gave the S&P 500 a lift overnight, dark clouds are gathering," strategists at OCBC Bank wrote in a note.
"With some signs of weakness in the European and Asian manufacturing PMIs Asian, markets may trade with a slightly more cautious tone."
IHS Markit purchasing managers' indices released on Monday showed manufacturing growth in the euro zone slowed to a two-year low at the end of the third quarter.
The United States and Canada forged a last-minute deal on Sunday to salvage NAFTA as a trilateral pact with Mexico, rescuing a $1.2 trillion open-trade zone that had been about to collapse after nearly a quarter century in operation.
The Dow rose 0.73 percent and the S&P 500 gained 0.36 percent on Monday after the deal to preserve NAFTA helped ease trade worries.
"There were concerns that the resulting confusion would exceed that of the U.S.-China trade row if NAFTA was scrapped. While it appears like Canada and Mexico caved in to the United States, the outcome is positive for global trade and the economy," said Yoshihisa Maruyama, chief market economist at SMBC Nikko Securities in Tokyo.
The Canadian dollar traded at C$1.2815 per dollar after rallying to a four-month high of C$1.2782 overnight following the trilateral trade pact.
The euro was little changed at $1.1543 after slipping 0.25 percent on Monday on renewed concerns about heavily-indebted Italy's budget.
The single currency has been hurt by concerns that a significant increase in the Italian budget will deepen Italy's debt and deficit problems.
The dollar was at 113.845 yen after scaling an 11-month high of 114.06 yen on Monday, as improving investor risk sentiment weighed on the Japanese currency.
The yen is usually seen as a safe haven at times of turmoil but recedes when risk appetite returns.
The dollar index against a basket of six major currencies rose 0.2 percent to 95.462, its highest since Sept. 10.
The greenback drew support from an uptick in U.S. Treasury yields as Wall Street gains curbed demand for safe-haven debt.
In commodities, U.S. crude futures were up 0.4 percent at $75.60 a barrel.
Crude contracts surged nearly 3 percent to $75.77 a barrel on Monday, their highest since November 2014, as the deal to salvage NAFTA stoked economic growth expectations, with impending U.S. sanctions on Iran seen raising prices.
Brent crude edged up 0.1 percent to $85.07 a barrel after rallying 2.7 percent the previous day to a $85.45, highest since November 2014.
Additional reporting by Tomo Uetake; Editing by Shri Navaratnam and Eric Meijer