Asian stocks were steady on Tuesday as Japanese equities rose to a fresh 27-year high while crude oil prices were elevated in the afterglow of an agreement that salvaged a North American free trade deal.

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The United States and Canada forged a last-minute deal on Sunday to salvage NAFTA as a trilateral pact with Mexico, rescuing a three-country, $1.2 trillion open-trade zone that had been about to collapse after nearly a quarter century.

MSCI's broadest index of Asia-Pacific shares outside Japan was little changed.

Australian stocks edged up 0.1 percent and South Korea's KOSPI added 0.05 percent. Japan's Nikkei gained 0.5 percent.

"The NAFTA deal is an achievement that President Trump managed to clinch before the US midterm elections, caution in the broader markets is receding for the time being," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management.

The Chinese financial markets are closed for the week of October 1-5 for national holidays.

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.

The Canadian dollar traded at C$1.2810 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 $1.1577 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 raise the country's debt levels.

The dollar hovered slightly below an 11-month high of 114.06 yen scaled on Monday, with improving investor risk sentiment weighing on the Japanese currency.

The dollar index against a basket of six major currencies stood at 95.289 following a rise to 95.373 overnight, its highest since September 10.

The greenback drew support thanks to an uptick in US Treasury yields as equity market gains curbed demand for safe-haven debt.

In commodities, US crude futures were up 0.35 percent at $75.56 a barrel.

The contracts had 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 and with US sanctions on Iran also looming.