* Greek T-bill auction well covered but with high yield
* Analysts say Greece still has tough times ahead
* Euro weighed in volatile session on Greek concerns
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NEW YORK, April 13 (Reuters) - The dollar rose against the euro on Tuesday after a Greek debt auction showed the market asked a high price to hold the assets and Greece's fiscal crisis would continue to weigh on the single currency.
Greece passed its first borrowing test since the euro zone agreed on a potential rescue package but the high premium paid was a sign it was likely to need financial aid.
On Monday, the euro climbed to a near one-month high of $1.3691 after euro zone finance ministers agreed on an aid package for Greece, before paring gains as investors sought clarification about the plan.
The dollar also gained on talk among traders that a U.S. think tank report said the Federal Reserve was closer to raising one of its key interest rates.
"The aid package is a band aid which does not resolve the Greeks' long-term issues," said John McCarthy, director of foreign exchange at ING Capital Markets in New York, of the euro's wild swings on Tuesday.
Midway through a volatile session in New York the euro was trading at $1.3558, down 0.2 percent on the day and just off a session low of $1.3552 EUR=>.
Greece easily sold its allocation of 6-month and 12-month T-Bills, raising 1.56 billion euros, with the inclusion of non-competitive bids, but at a yield which was costly for the debt-laden country. ID:nLDE63C0FQ
The euro rose briefly in the immediate aftermath of the auction as traders reacted to a strong bid to cover ratio.
However, analysts said attention then shifted to the yield Greece had to pay -- more than double those paid at auctions in January of bills with similar maturities.
"With the Greek bill auction behind it, the market may lack a clear focus, but sentiment towards the euro remains poor, even though there had been some short-covering in the futures market in the most recent reporting week," said Marc Chandler, global head of foreign exchange strategy at Brown Brothers Harriman in New York.
Against the yen EURJPY=>, the euro slipped to trade down 0.1 percent at 126.50 yen, staying above its overnight low of 125.71, hit as investor caution crept in regarding the Greek aid plan.
The draft of a policy paper from Japan's ruling party, released early in the European morning, initially put the Japanese currency under pressure before focus shifted to other risks and events.
The draft suggested the dollar JPY=> should be kept around 120 yen. This pushed the greenback to the day's high at 93.42 yen. ID:nTKG006692. It last traded up 0.1 percent at 93.31 yen.
But it was a also a turbulent session for the dollar/yen pair with the U.S. currency falling to its lowest in two weeks against the yen in Asia trading. Some said a report that the Bank of Japan may slightly revise up its consumer price forecast for the next fiscal year helped the yen.
Bank of Japan Governor Masaaki Shirakawa later said annual consumer price falls were expected to narrow as the output gap shrinks but also that the central bank did not rule out any policy option. ID:nTKF106909
(Reporting by Nick Olivari; Editing by Andrew Hay)