MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.3%. Japan's Nikkei bucked the trend with rise of a 0.5%, though it was still down on the week so far.
Oil prices remained near nine-month highs after militants from the Islamic State of Iraq and the Levant (ISIL) group seized a large swathe of northern Iraq and threatened to capture a key oil refinery. The insurgent advance forced Washington to not only consider options for military action but also hold brief talks with Iran, its long-time foe, to support the besieged government in Baghdad.
US crude futures edged down on Tuesday to $106.76 per barrel after having climbed as high as $107.68 on Friday, but investors remain wary of potential disruptions to oil exports.
"The advance of extremists to Baghdad or bombing by US forces will be a trigger to justify rise in US oil prices above $110. That would be a burden for the world economy in the near term," said Daisuke Uno, chief strategist at Sumitomo Mitsui Banking Corp.
Higher energy costs are likely to curb growth in oil-importing economies, with the Indian rupee already falling victim to worries over rising inflation to hit a one-month low on Monday.
Tension in Ukraine showed no sign of abating as Russia cut off gas to Ukraine on Monday in a dispute over unpaid bills that could disrupt supplies to the rest of Europe and set back hopes for peace between the former Soviet neighbours.
As investor risk sentiment was hit, flight-to-quality bids underpinned US Treasuries prices despite solid US industrial output data on Monday. The 10-year yield stood at 2.593%, off last week's peak of 2.662%.
Immediate focus is on the Federal Reserve's monetary policy statement on Wednesday, when the US central bank is expected to announce it will continue paring its bond purchase programme and cut its growth projections.
In the currency market, the Australian dollar slipped after minutes of the Australian central bank's June 3 meeting were more dovish than expected.
The Aussie dipped 0.4% to $0.9361 as the minutes showed the Reserve Bank of Australia was not sure the current stimulus would be enough to offset a drag from falling mining investment and government belt-tightening.
The British pound held near a five-year high hit on Monday, maintaining momentum after Bank of England chief Mark Carney surprised markets last Thursday by suggesting the Bank of England may tighten its policy before year-end.
The pound stood at $1.6975, near Monday's high of $1.7011, with close attention falling on consumer inflation data due later in the day given the focus on the BoE's policy.
Elsewhere, Argentina's Merval index fell 10.1% on Monday after the US Supreme Court declined to hear the country's appeal over its battle with hedge funds that refused to take part in its debt restructurings. The move risks sending Argentina into a fresh sovereign default, although Argentine shares have risen 34% so far this year.