Asian stocks slipped on Tuesday amid growing worries this month's referendum in Britain could see it exit the European Union, while markets were also nervous ahead of the U.S. Federal Reserve's two-day meeting that begins later in the day.

The pound and euro have suffered in recent sessions as economists fear that the so-called Brexit would tip Europe back into recession. Voters appear divided ahead of the June 23 referendum, with the "Out" campaign widening its lead over the "In" camp, according to two opinion polls published by ICM on Monday.

MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.4 percent in early trade, after Wall Street lost ground for the third straight session.

Japan's Nikkei stock index slipped to two-month lows in choppy trade, and was off 0.2 percent after tumbling 3.5 percent on Monday.

Uncertainty over this week's Federal Open Market Committee policy meeting has weighed on markets, though the U.S. central bank is widely expected to leave rates unchanged after the much weaker-than-expected May nonfarm payrolls report.

"The committee was actively preparing markets for a June-July rate hike until the release of the May employment report and is unlikely to give up its tightening bias absent additional information that labor markets are weakening," analysts at Barclays wrote.

"Nevertheless, the abrupt slowing in employment and falling long-run inflation expectations should raise alarm bells, and risk management concerns suggest delaying action until after the outcome of the UK referendum," they said.

The Bank of England, Swiss National Bank and the Bank of Japan will also meet this week, and are similarly expected to stand pat on policy with the Brexit vote looming.

The dollar index, which tracks the greenback against a basket of six rival currencies, edged up 0.1 percent to 94.419, moving back toward the overnight high of 94.750. That was its highest since the downbeat U.S. jobs report toppled the dollar on June 3.

The perceived safe-haven yen has benefited from investors' risk aversion. The dollar edged down 0.1 percent to 106.16 yen, moving back toward Monday's low of 105.735, its weakest level since early May.

The euro was down 0.1 percent at $1.1286. Against the yen, it skidded 0.2 percent to 119.88, moving back toward a more than three-year low plumbed in the previous session.

Sterling also notched a three-year low against the yen on Monday, and was last down 0.3 percent at 151.11 yen. Against the dollar, the pound dropped 0.4 percent to $1.4209.

Crude oil prices continued to slip, pressured by the strong U.S. dollar and worrying economic prospects in Europe and Asia, though losses were contained by ongoing supply outages in Nigeria.

Brent was down 1 percent at $49.83 per barrel, while U.S. crude also shed 1 percent to $48.37.