* Dollar index rises to highest since mid-December * Worries about more budget wrangling drive safety demand * Yen rises versus dollar, euro after recent weakness By Wanfeng Zhou NEW YORK, Jan 3 (Reuters) - The dollar climbed to a three-week high against a basket of currencies on Thursday as concerns about more budget wrangling in Washington drove investors to the more liquid U.S. currency. While lawmakers reached a deal to avert the "fiscal cliff" of huge tax hikes and spending cuts, the agreement set up potentially bruising showdowns over the next two months on spending cuts and an increase in the nation's limit on borrowing. "We really just kicked the can down the line and we're set up for another flight on the hill in the next month and a half or so," said John Doyle, currency strategist at Tempus Consulting in Washington. "That put a damper on overall risk appetite." The dollar index, which tracks the greenback versus six major currencies, rose to 80.229, the highest since Dec. 11. It was last up 0.3 percent at 80.114. "There could be a messy two months ahead and we see the dollar index reclaiming some ground," said Jane Foley, senior currency strategist at Rabobank. Investors often see the U.S. currency as a safe haven and buy it during times of market uncertainty, even when that uncertainty stems from the United States. Highlighting market concerns that the U.S. deficit issues remain unresolved, ratings agency Moody's Investors Service said the United States must do more to rescue its Aaa debt rating from its current negative outlook. Standard & Poor's said the fiscal deal does not affect its negative view of the U.S. credit outlook, and said more work remains ahead for policymakers. The euro fell 0.6 percent to $1.3108. It had earlier fallen to $1.3082 according to Reuters data, the weakest since Dec. 14, after stop-loss sell orders were triggered below $1.3090. Traders said the euro's failure to break above $1.33 in the previous session drew sellers into the market. Strategists also said the current weakness in the euro could persist as the euro zone economy falls deeper into recession and on increasing prospects of an interest rate cut by the European Central Bank. The euro fell 1.1 percent to 113.90 yen as investors took profits on its rise to an 18-month high of 115.99 yen on Wednesday. "Euro/yen at around 115 levels was starting to look a bit overdone and the euro may actually lose ground against the yen in the coming weeks. It's moved too far too fast," said Colin Asher, senior economist at Mizuho Corporate Bank. The dollar fell 0.6 percent to 86.84 yen, after climbing as high as 87.36 earlier in the global session, the highest since July 2010. Over the past few weeks, the yen has weakened on expectations that a new Japanese government led by Prime Minister Shinzo Abe will push the Bank of Japan into further monetary easing to beat deflation. Analysts said the yen is likely to remain vulnerable until the BOJ's policy meeting on Jan. 21-22. The dollar briefly cut losses against the yen and gained versus the euro after data showed U.S. private-sector employers added more new jobs than expected last month even as a possible budget crisis loomed. Separate data showed U.S. initial jobless claims rose last week. Later in the session, the Federal Reserve will release the minutes of its latest policy meeting. On Friday, the U.S. government will release its closely watched monthly nonfarm payrolls report.