* Nikkei probes highest levels since November 1991
* U.S. crude oil futures rise to highest since May 2015
TOKYO, Jan 9 (Reuters) - Asian shares edged higher on Tuesday, approaching record highs after the S&P 500 extended its winning streak, while the dollar steadied against its major counterparts.
MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.1 percent at 590.23, not far from its record peak of 591.50 scaled in November 2007.
On Wall Street on Monday, the Dow Jones Industrial Average edged down 0.05 percent, the S&P 500 gained 0.17 percent, and the Nasdaq Composite added 0.29 percent. After the best start to a year in more than a decade, investors turned cautious ahead of earnings.
Japan's Nikkei stock index rose 0.8 percent to its highest levels since November 1991, catching up to the previous session's gains as markets reopened after a holiday on Monday.
The dollar index, which tracks the greenback against a basket of six major rival currencies, was steady on the day at 93.348.
The euro was steady at $1.1967, not far from its nearly four-month high of $1.2089 set on Thursday.
Against the yen, the dollar edged up 0.1 percent to 113.14 .
Underpinning the dollar, investors bet on further U.S. interest rate hikes after Friday's payrolls data did nothing to challenge the outlook for monetary policy tightening by the U.S. Federal Reserve. While job growth slowed more than expected, a pickup in monthly wages pointed to labor market strength.
"Broadly, viewed in context, it was still a reasonably strong labor market," said Bill Northey, chief investment officer at the private client group of U.S. Bank in Helena, Montana.
"There was nothing in there to dissuade us from the view that the Fed will move again, appropriately, likely in March," he said.
But the dollar's upward momentum was tempered as investors differed on the pace of tightening while U.S. inflation remains relatively cool.
Atlanta Fed President Raphael Bostic, who is a voting member of the central bank's policy board, said on Monday that only two hikes might be needed in 2018, in light of weak price pressures.
U.S. crude oil prices firmed to their highest levels since May 2015, as political concerns in some OPEC nations offset projections for higher U.S. oil production.
Brent had not yet traded in Asia, while U.S. crude rose 43 cents, or 0.7 percent, to $62.17 a barrel.
Spot gold was down 0.2 percent at $1,317.66 an ounce, pulling back from a 3-1/2-month high hit last week.
(Reporting by Lisa Twaronite; Editing by Sam Holmes)