North Korea's foreign minister said on Monday that a weekend tweet by President Donald Trump counted as a declaration of war on North Korea and that Pyongyang reserved the right to take countermeasures, including shooting down US bombers even if they are not in its air space.
MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.2 percent in early trade, following losses on Wall Street.
Australian shares were up 0.1 percent, while South Korean shares were 0.3 percent down.
Japan's Nikkei stock index sagged 0.2 percent, pressured by a stronger yen.
"In addition to North Korea, the stronger yen is affecting shares today, and there's also Apple's poor performance, after the report that it told suppliers to reduce parts shipments," said Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities.
Apple Inc shed 0.9 percent on Monday after it was reported the company had told suppliers to scale back shipments of parts for its upcoming iPhone X.
The dollar was slightly down against the yen at 111.70 and well shy of last week's two-month high of 112.725.
The yen tends to benefit during times of risk aversion due to Japan's net creditor status and the expectation that Japanese investors would repatriate assets when facing a crisis.
The euro edged up after tumbling on Monday following a severely diminished election victory for German Chancellor Angela Merkel that was accompanied by a surge in support for the far right.
Support for Merkel's conservatives unexpectedly slumped to its lowest since 1949 and the Social Democrats, partners in the outgoing coalition, said they would go into opposition.
The single currency was 0.1 percent higher at $1.1856 , while the dollar index, which tracks the greenback against a basket of six major rivals, was down 0.1 percent at 92.601.
Later on Tuesday, Federal Reserve Chair Janet Yellen is scheduled to speak on "Prospects for Growth: Reassessing the Fundamentals" at 1645 GMT.
On Monday, New York Fed President William Dudley said the US central bank is on track to gradually raise rates given factors depressing inflation are "fading" and the US economy's fundamentals are sound.
But Chicago Fed President Charles Evans said the Fed should wait until there are clear signs of faster wage and price growth before hiking rates again.
Crude oil prices gave back some of their gains after soaring more than 3 percent on Monday, with Brent hitting its highest in more than two years. Major producers said the global market was on its way to rebalancing, while Turkey threatened to cut oil flows from Iraq's Kurdistan region to its ports.
US crude eased 0.2 percent to $52.12 a barrel, after touching its highest levels since April on Monday. Brent crude edged up 0.1 percent to $59.10, after scaling its highest peak overnight since July, 2015. —Reuters
