Asian stocks mostly edged lower on Tuesday, while the cost of oil pulled back, as the selling sparked by the crisis in Ukraine moderated.

Although Japan and South Korea continued to weaken, the moves were small, as the situation in Ukraine hadn't deteriorated significantly and stocks had already sold-off in the previous session. On Monday, Ukraine accused the Kremlin of taking border posts and increasing the size of its forces in the Crimea.

Japan's Nikkei fell by 0.3% as the yen softened slightly against the dollar in Asian trade. The dollar was last at Yen101.53 compared with Yen101.44 late Monday in New York.

"The immediate and likely largest impact from the risk-off sentiment due to the crisis in the Ukraine may have already passed," said Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities.

Elsewhere in the region, South Korea's Kospi was down just 0.2% and Australia's S&P/ASX 200 added less than 0.1%.

The price of oil, which had jumped 2.3% on Monday, also eased early on Tuesday. Nymex crude fell by 0.2% to $104.70 a barrel.

The situation in the Ukraine is the latest crisis to hurt sentiment this year, and the performance of global markets overnight was broadly negative with stocks in both the U.S. and Europe dropping on Monday. Russia was hit the worst, as the Micex index plunged 11% and the ruble touched a record low against the dollar.

Asia has already weathered shocks from a number of emerging markets in 2014, which has put much of the region in the red for the year. Most notably, investors were spooked by concerns over unrest in Turkey and renewed fears over the state of China's economy. As a result, stocks spent much of February recovering from a sell-off that started in January.

Brad Frischkorn contributed to this article.

Write to Daniel Inman at daniel.inman@wsj.com

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