The British pound remained fragile near a two-month low against the dollar and the yen hovered near six-week highs against the U.S. currency on worries Britain may leave the European Union in a referendum less than 10 days away.

Two recent opinion polls show a lead for the "Leave" campaign. While many market players are skeptical about the polling, recent poll results do seem to suggest a momentum for "Leave," market players said.

The British pound dropped almost 0.5 percent in volatile early Asian trade to $1.4203, after having fallen to a two-month low of $1.4117 on Monday.

"Although those opinion polls were not necessarily reliable in the case of Scotland's referendum on its independence, the markets have been swayed by them recently," said Hideki Kishida, fixed income analyst at Nomura Securities.

As investors readied for a plunge in the pound by buying pound put options, implied volatilities continued to soar, with one-month volatility hitting an unprecedented level around 28 percent.

Against the yen, which tends to rise at times when risk appetite falls, partly because of Japan's net creditor status, the pound fell to as low as 149.50 yen on Monday and last stood at 150.80 yen.

The yen is the strongest among G10 currencies so far this month, and held at 105.975 per dollar, near Monday's six-week high of 105.735 to the dollar. A break of that level could lead to a test of its 18-month high of 105.55 set on May 3.

The yen also stood near a three-year high against the euro, which traded at 120.02 yen after having fallen to 119.005 on Monday, a level last seen in February 2013.

The euro traded at $1.1291, having recovered from Monday's low of $1.1233.

The euro is also vulnerable to threats of Brexit, which would hurt the euro zone economy and deal a serious blow to European integration.

At the same time, however, the currency could be helped by safe-haven flows as the euro is often used as a funding currency for bets in riskier assets.

Surprisingly soft U.S. employment data published earlier this month quashed expectations of a near-term rate hike by the U.S. Federal Reserve, underpinning the euro and other currencies against the dollar.

The Federal Reserve is set to meet on Tuesday and Wednesday, with market players waiting for clues about when the Fed might next look to move on rates.

"Because of weak U.S. job data, the earliest the Fed can raise rates will be September," said Minori Uchida, chief currency analyst at the Bank of Tokyo-Mitsubishi UFJ.