By Satomi Noguchi TOKYO (Reuters) - The dollar fell against the euro on Monday, giving up some of its gains made after the U.S. government offered a lifeline to Detroit carmakers, as investors remained concerned over the deepening economic recession. The dollar had posted its biggest daily gain against the euro in almost two months on Friday, with traders saying the U.S. currency's slump after the Federal Reserve's interest rate cut to near zero earlier in the week was probably overdone. Dealers said the U.S. rescue of General Motors Corp (GM.N) and Chrysler LLC CBS.UL had averted a crisis for now, but uncertainty remained over how the companies' restructuring plans demanded in return for the bailout would impact the economy already in a deep and long recession. "The picture that the currency market is painting for the U.S. economy next year is not as hopeful as the one in the stabilizing stock markets," said Kengo Suzuki, a currency strategist at Shinko Securities. "Last week's dollar slump was too much too fast, but the market is pointing that the next trend is in that direction," Suzuki said. The euro rose 0.5 percent from late New York trade on Friday to $1.3972 after falling to as low as $1.3824, according to EBS. It soared as high as $1.4720 on EBS on Thursday. "The Fed is about to go and print money, boosting dollar supply to support the economy. It is not hard to imagine the dollar's value falling from here on," said a chief fund manager at a Japanese asset management firm. "Given the outlook for currencies, bonds in the euro zone look relatively attractive with their higher yields, if one had to choose between them and U.S. Treasuries," the fund manager said. The yield on 10-year U.S. Treasuries fell to a five-decade low near 2 percent last week while the 10-year Bund yield also hit its lowest since at least 1999, but traded around 3 percent. The sudden reversal in the euro's sharp gains late last week was triggered after the European Central Bank said it would reduce the return it offers to those banks that hold cash with it. That revived speculation of a further ECB interest rate cut in January to combat a recession in the euro zone economy. But recent comments by council members have suggested the bank may be divided on the best near-term course of action, an impression reinforced by remarks made by ECB Executive Board member Lorenzo Bini Smagi in a newspaper interview. The dollar rose versus the yen, holding gains made late last week after the Bank of Japan lowered its policy rate down close to zero, mirroring the Fed move. The U.S. currency rose 0.8 percent to 90.04 yen, off a 13-year low of 87.13 yen touched last week. Data on Monday showed Japan's exports fell by a record in November from a year earlier as a rapid deterioration in global economic conditions deals a heavy blow to the world's second-largest economy. A Reuters poll showed Japanese manufacturers' business sentiment hit a historic low in December and logged the sharpest month-on-month drop on record, reinforcing expectations that the BOJ might yet to be forced to do more, capping the yen's advance, some traders said. Continued...

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