The U.S. dollar strengthened against the other major currencies in the Asian session on Tuesday amid rising speculation on an interest rate hike by the U.S. on the back of optimistic comments by Federal Reserve Vice Chairman Stanley Fischer and Cleveland Federal Reserve Bank President Loretta Mester.

In a speech to a college in a suburb outside Tel Aviv in Israel on Monday, Fischer said that central bankers are weighing the risk of raising rates prematurely.

Fischer also noted that the timing for the first rate increase would depend on the pace of economic growth.

"Our process is not date-determined. They are data-determined," he said.

In an interview in Reykjavik, Iceland, Mester said that 'time is near' for a rate hike.

"If the data comes in according to my forecasts then the time is near where we're going to be wanting to raise rates," Mester said.

She also said that the FOMC will go into its June meeting with an 'open mind' about rate hikes.

Friday's better-than-expected U.S. inflation data and comments made by Fed Chair Janet Yellen about interest rates also increased expectations of interest rate normalization.

U.S. markets will open on Tuesday after Monday's Memorial Day holiday, with U.S. durable goods, housing and consumer confidence reports due later in the day.

Friday, the U.S. dollar rose 0.29 percent against the euro, 0.08 percent against the pound and 0.17 percent against the yen.

In the Asian trading today, the U.S. dollar rose to a 2-1/2-month high of 121.78 against the yen and nearly a 1-1/2-month high of 1.2327 against the Canadian dollar, from yesterday's closing quotes of 121.54 and 1.2307, respectively. If the greenback extends its uptrend, it is likely to find resistance around 122.80 against the yen and 1.28 against the loonie.

Against the euro, the pound and the Swiss franc, the greenback advanced to a 4-week high of 1.0930, more than a 2-week high of 1.5431 and nearly a 4-week high of 0.9473 from yesterday's closing quotes of 1.0976, 1.5466 and 0.9445, respectively. On the downside, 1.06 against the euro, 1.50 against the pound and 0.98 against the franc are seen as the next resistance level for the greenback.

Looking ahead, U.S. durable goods orders for April, U.S. S&P Case-Shiller's house price index for March, the Conference Board's U.S. consumer confidence index for May and new home sales data for April are due to be released in the New York session.

At 12:30 pm ET, Federal Reserve Governor Stanley Fischer is expected to speak on "The Federal Reserve and the Global Economy" before a conference in honor of Professor Haim Ben-Shaharat at the Tel Aviv University in Israel.

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