The U.S. dollar firmed against its major counterparts in European trading on Tuesday, as hawkish speeches by several regional Fed presidents overnight cemented hopes that the central bank will raise rates as early as next month.

Traders focus on speech by U.S. Federal Reserve Chair Janet Yellen later this week, to gauge more clues about a potential interest rate hike in June.

Federal Reserve Bank of Philadelphia President Patrick Harker joined the chorus of other fellow Fed members on Monday, saying the Fed is likely to raise interest rates at a mid-June policy meeting unless the economic growth deviates from positive track.

"I can easily see the possibility of two or three rate hikes over the remainder of the year," he told.

The Fed is moving closer to "slow normalization" of interest rates, St. Louis Fed President James Bullard said in Beijing Monday.

"By nearly any metric, U.S. labor markets are at or beyond full employment," Bullard said. "This may put upward pressure on inflation going forward."

San Francisco Fed President John Williams said there could be two or three rate hikes this year.

The Fed officials will convene a 2-day policy meeting on June 14-15 to decide whether the economy is strong enough to cope up with another rate hike.

The dollar was trading mixed in Asian deals. While the currency rose against the franc and the euro, it held steady against the pound and the yen.

The greenback appreciated to 2-1/2-month high of 0.9932 against the franc, and held steady thereafter. The pair finished yesterday's trading at 0.9893.

Data from the Federal Customs Administration showed that Switzerland's trade surplus increased in April as exports recovered amid a fall in imports.

The trade surplus increased to CHF 2.5 billion in April from CHF 2.2 billion in March.

Reversing from an early low of 1.1227 against the euro, the greenback strengthened to a 2-month high of 1.1157. Further uptrend may lead the greenback to a resistance around the 1.10 mark.

Survey from the Centre for European Economic Research or ZEW showed that Germany's economic sentiment weakened for the first time in three months, defying expectations for improvement as financial experts do not expect the strong performance of the economy in the first quarter to continue.

The ZEW Indicator of Economic Sentiment for Germany dropped to 6.4 from 11.2 in April. Economists had forecast a score of 12. The index declined for the first time since February.

The greenback edged up to 109.77 against the Japanese yen, after having fallen to 109.17 at 2:05 am ET. On the upside, 112.00 is likely seen as the next resistance level for the greenback.

Extending early rally, the greenback firmed to 0.7145 against the aussie, its strongest since March 1. The greenback is seen challenging resistance around the 0.70 region.

On the flip side, the greenback slipped to a 5-day low of 1.4622 against the pound, compared to 1.4483 hit late New York Monday. The greenback may test support around the 1.48 area.

Bank of England Governor Mark Carney said the bank is responsible to warn Britons about the risks that would arise if people vote to leave EU in the referendum on June 23.

The central bank has responsibility to the British people, who don't want risks kept from them, Carney said at the parliament's Treasury Select Committee

The U.S. new home sales data for April and U.S. Richmond Fed manufacturing index for May are set to be published in the New York session.

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