* April Fed minutes raise prospect of near-term hike
* Euro hits weakest since late March
* Japanese exporters' offers may temper dollar/yen rise (Updates prices, adds more comment)
By Patrick Graham
LONDON, May 19 (Reuters) - The dollar steadied at its highest levels since March on Thursday after a perceived increase in chances of a rise in U.S. interest rates by September drove its biggest daily gain against the euro in five weeks.
Stronger data, rhetoric from the Federal Reserve and a resulting shift on money markets has revived expectations among hedge funds of a new rally for the U.S. currency, which came within sight of parity with the euro a year ago.
Yet in a U.S. election year, and with markets suspicious that political uncertainty has played a role in the dollar's slide since February, caution abounds.
Many speculative players have been disappointed over the past year by the U.S. currency's failure to rise and the most recent data from last week shows the market overall now betting net on a weaker dollar.
"A lot of investors even today still want to keep the long dollar position in the portfolio. The reason is still simple: the monetary policy gap is there but a lot of people have been hurt," said James Kwok, head of currency management at French asset managers Amundi.
He has been cautious of backing the dollar against other major currencies, preferring to play it against Asian currencies including China's yuan, the Singapore dollar and Korean won.
"We think the dollar will continue to go up, but it will not be broad-based any more," he said.
"It will not be against most of the currencies that people expect, not against the currencies whose central banks have tried hard to weaken through QE, negative rates and so on. You can see how dangerous it has become to bet against the yen."
The dollar inched up to as high as $1.1202, adding just a hundredths of a cent to levels hit in the previous session. EUR= .
"I don't think another broad-based rally is off the table," said Tony Bedikian, Managing Director of Global Markets with Citizens Bank in Boston.
"It will be driven by the relative policy biases. If the ECB continues stimulus and the U.S. moves towards a more tightening policy, then I think you will see more dollar strength. But it is going to be interest rate dependent."
Gains against the Canadian and New Zealand dollars CAD= NZD= pushed the dollar 0.2 percent higher against a basket of currencies that measures its broader strength .DXY but it was also a third of a percent lower at 109.83 yen.
Traders in Tokyo saw the potential for dollar-selling by Japanese exporters like Toyota 7203.T and Honda 7267.T , who have both assumed average dollar rates of 105 yen in 2016/17. meeting of G7 finance leaders in Sendai, northern Japan on Friday and Saturday is expected again to expose a rift on issues ranging from currency intervention to fiscal policies within the group of advanced economies. officials have warned regularly against "one-sided" moves in the yen, but most analysts believe U.S. opposition will prevent them intervening against the currency.
(Editing by Catherine Evans)