In the U.K., two new polls showed public opinion over a Brexit remained divided. An ORB poll for the Telegraph showed 48 percent of Britons would vote to remain in the European Union, while 49 percent would vote to leave.
A YouGov poll for the Times of London showed 46 percent preferred to leave, while 39 percent wanted to remain. Popular British newspaper The Sun also endorsed the leave vote for the upcoming referendum vote on June 23.
Gareth Nicholson, an investment manager at Aberdeen Asset Management Asia told CNBC's "Squawk Box" that whichever way the Brexit vote goes, market volatility will increase. "Markets are getting concerned ... volatility is not good for the broader market. That's why you see weakness in foreign exchange and equity."
The British pound traded at $1.4146 in the afternoon Asia time, compared with levels around $1.4600 in late May.
Markets will also be watching the U.S. Federal Open Market Committee (FOMC), which begins its two-day meeting starting on Tuesday.
Kit Juckes, global fixed income strategist at Societe Generale, said in a note Monday the market did not expect the Fed to raise rates.
"The challenge for the Fed is how to continue laying the groundwork for an eventual hike if the data bounce back from the disappointment of May payrolls, against the backdrop of nervous markets," he said.
The Bank of Japan (BOJ) starts its two-day meeting on Wednesday, June 15. HSBC economist Izumi Devalier expects the BOJ to ease policy this week. "The longer the board waits to address downside risks to the economy and prices, the more markets will question the central bank's commitment towards its inflation target," she said in a note.
Devalier added, "Reduced market confidence in the BOJ's inflation commitment could then feed back into a stronger yen (as it did after the April policy meeting), making the central bank's job even more difficult."
Elsewhere, oil prices failed to hold onto the psychologically key $50 level, with U.S. crude down 0.96 percent at $48.41 a barrel as of 2:52 p.m. HK/SIN. Global benchmark Brent was down 0.81 percent at $49.94.
The dollar traded at 94.506 against a basket of currencies as of 2:53 p.m. HK/SIN, up from levels near 93.500 in the previous week.
"Perhaps, there is a degree of market wariness ahead of the FOMC [meeting], which has stymied dollar strength given the possibility of another dovish shift in message or dots," said Wei Liang Chang, a foreign exchange strategist at Mizuho Bank.
Stateside, the Dow Jones industrial average closed down 132.86 points, or 0.74 percent, at 17,732.48; the S&P 500 was down 17.01 points, or 0.81 percent, at 2,079.06. The Nasdaq composite finished down 46.11 points, or 0.94 percent, at 4,848.44.
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