Australian stocks were down 0.35 percent after briefly touching a four-month high and South Korea's KOSPI shed 0.55 percent. Japan's Nikkei was a shade lower, its surge to a three-month peak bogging down.
Hong Kong's Hang Seng lost 0.5 percent, pulling back from a two-month peak to snap a five-day winning run and Shanghai inched up 0.05 percent.
Investors in Chinese equities will likely re-jig their exposure after MSCI, the U.S. index publisher, published its latest index weighting.
MSCI said on Tuesday that 234 Chinese large caps will be partially included in its global and regional indexes on June 1, following an index review ahead of China's inclusion in MSCI's widely tracked equity benchmarks.
Wall Street scraped out gains on Monday after weakness in defensive stocks offset optimism following U.S. President Donald Trump's conciliatory remarks toward China's ZTE Corp that helped calm U.S.-China trade tensions.
While higher oil prices sometimes raise inflation concerns, the recent crude oil surge - Brent has risen 17 percent so far in 2018 - was seen to be generally supportive for equities.
"The recent rise in prices of crude oil won't have a broadly negative impact on equity markets if it continues at the current pace," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management in Tokyo.
"The rise in oil prices is boding well for certain stock sectors like energy shares."
Brent crude added 4 cents to $78.27 a barrel and in close reach of $78.53, the 3-1/2-year high marked on Monday. U.S. crude oil futures advanced 0.4 cents to $71.00 a barrel and in reach of $71.89, the highest since November 2014 scaled on Thursday.
Oil prices received their latest lift as OPEC reported that the global oil glut has been virtually eliminated. Tensions in the Middle East and uncertainty about output from Iran amid renewed U.S. sanctions have contributed to the recent rise in oil prices.
"The commitment of Saudi Arabia and the rest of OPEC to the production cuts is a major factor in supporting the price at the moment as well as the possibility of reduced exports from Iran due to sanctions," said William O'Loughlin, investment analyst at Rivkin Securities.
In currencies, the dollar index against a basket of six major currencies nudged up 0.05 percent to 92.643.
The greenback took a knock against the euro earlier on Monday after European Central Bank policymaker Francois Villeroy de Galhau said the ECB could give fresh timing guidance of its first rate hike as the end of its exceptional bond purchases approaches.
The U.S. currency managed to bounce back, however, after Cleveland Federal Reserve President Loretta Mester reiterated support for gradual interest rate increases.
The euro stood little changed at $1.1933 after pulling back sharply from the previous day's high of $1.1996.
The dollar was a shade higher at 109.745 yen, adding to the previous day's gains.
The currency drew support as U.S. Treasury yields rose amid the easing of U.S.-China trade tensions.
The 10-year Treasury note yield was at 2.998 percent after rising about 2.5 basis points overnight. (Reporting by Shinichi Saoshiro Additional reporting by Henning Gloystein in Singapore Editing by Shri Navaratnam and Sam Holmes)
© Reuters News 2018