* Dollar firms as upbeat data reinforces rate hike expectations
* Crude oil futures extend losses after overnight tumble
TOKYO, Oct 3 (Reuters) - Asian shares tiptoed lower on Tuesday, pressured by weaker oil prices but supported by records on Wall Street and upbeat economic data that lifted U.S. Treasury yields and the dollar.
MSCI's broadest index of Asia-Pacific shares outside Japan percent was down 0.1 percent in early trade.
Japan's Nikkei stock index added 0.3 percent, getting a tailwind from a weaker yen.
Australian shares slipped 0.4 percent ahead of the Reserve Bank of Australia's (RBA) policy decision. While no monetary steps are expected, investors will be looking to see if the central bank adopts a more hawkish bias.
On Wall Street on Monday, U.S. stocks started the fourth quarter on a strong note, with all three major indexes closing at record highs after data underscored strength in the economy.
A measure of U.S. manufacturing activity surged to a near 13-1/2-year high in September. Disruptions to the supply chains caused by Hurricanes Harvey and Irma resulted in factories taking longer to deliver goods and boosted raw material prices.
The Institute for Supply Management index rose to 60.8 in September, from 58.8 in August, exceeding expectations for a reading of 58.
U.S. construction spending also rebounded in August after two straight months of declines, boosted by increases in both private and public outlays.
The dollar stood tall, hoisted by rising U.S. Treasury yields. The yield on the benchmark 10-year note hit its highest since mid-July after the upbeat data reinforced expectations that the Federal Reserve will increase U.S. interest rates in December for a third time this year.
"There are strengthening expectations about what the Fed will do for the balance of the year, namely one more rate increase and balance sheet reduction," said Bill Northey, chief investment officer at U.S. Bank Private Client Group in Helena, Montana.
Due to the impact of the recent hurricanes, Northey said, "we're going to get some data anomalies over the next few months, but as you step back and take a broader context around trends that exist right now, it is clear the U.S. economy is performing very well, and it will continue to be on an improving path."
The dollar index, which tracks the greenback against a basket of six major rivals, added 0.1 percent to 93.650, nudging up to its highest levels since late August.
The euro was steady on the day at $1.1731, but still faces pressure from Spain's biggest constitutional crisis in decades, after Sunday's violence-marred independence referendum in Catalonia opened the door for its wealthiest region to move for secession as early as this week.
The dollar was nearly unchanged against its Japanese counterpart at 112.72 yen, within sight of last week's two-month high of 113.26 yen.
Proposed U.S. tax code changes as well as the possibility that U.S. President Donald Trump will appoint a more hawkish Fed Chair also gave the dollar a lift.
Crude oil futures edged down after tumbling on Monday, as a rise in U.S. drilling and higher OPEC output put the brakes on their recent rally.
Brent crude slipped 0.2 percent to $56.01 a barrel, after marking a third-quarter gain of about 20 percent. U.S. crude edged down 0.1 percent to $50.51.
Spot gold edged up slightly to $1,271.55 per ounce, after plumbing its lowest in nearly seven weeks on Monday as the dollar rose.
(Reporting by Lisa Twaronite; Editing by Sam Holmes)