* Monday's China growth figures continue to underpin sentiment
* Fading expectations of U.S. rate hike this year hit dollar
TOKYO, July 18 (Reuters) - Asian shares stepped back from more than two-year highs on Tuesday while the dollar sagged on growing expectations that the Federal Reserve will take a more cautious approach to raising interest rates.
MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.2 percent, a day after scaling its loftiest levels since April 2015.
Wall Street ended little changed on Monday in low-volume trading, as investors braced for a flood of second-quarter earnings reports later this week.
Japan's Nikkei stock index dipped 0.4 percent in early deals, as markets resumed trading after a public holiday on Monday and caught up to a stronger yen.
The dollar edged down 0.1 percent on the day to 112.53 yen , well below its nearly four-month high of 114.495 touched last week.
The euro was steady at $1.1477, while the dollar index, which tracks the greenback against a basket of six major rivals, wallowed at 95.131, not far from Monday's 10-month low of 95.018.
"It's hard to be bullish on the dollar, both from the monetary side and from the U.S. politics side," said Masafumi Yamamoto, chief currency strategist at Mizuho Securities.
Fading support for U.S. President Donald Trump is also weighing on the dollar, he said, as the U.S. administration tries to gather enough backers in the Senate to pass legislation to dismantle and replace the Affordable Care Act, commonly known as Obamacare.
"Trump's falling popularity, although it was not spectacular from the beginning, is another hurdle for pushing for the changes, and that will be negative for the U.S. economy and the dollar," said Yamamoto.
Fed funds futures continue to show less than a 50 percent chance of a rate hike in December after Fed Chair Janet Yellen sounded a cautious tone last week in her congressional testimony, and after downbeat U.S. inflation and retail sales data on Friday.
Overall Asian sentiment remained underpinned by solid China data on Monday, which showed its economy expanded at a faster-than-expected 6.9 percent clip in the second quarter, setting the country on course to comfortably meet its 2017 growth target.
Crude oil futures edged higher, with U.S. crude rising 0.2 percent to $46.10 per barrel and Brent crude adding 0.1 percent to $48.49.
Crude prices had skidded about 1 percent on Monday as investors held out for strong indications that an OPEC-led effort to drain a glut was proving effective.
(Reporting by Lisa Twaronite; Editing by Shri Navaratnam)