* Euro dips, some see its recent rise as overdone
* U.S. budget talks main focus in year-end trades
* Dollar steady after hitting 2-year high vs yen
* Currency moves volatile due to thin liquidity
By Anooja Debnath
LONDON, Dec 28 (Reuters) - The euro fell against the dollar on Friday, the last full day of trading for the year in Europe, as investors took profit on its recent gains, while investors focused on U.S. budget talks.
The euro was down 0.4 percent on the day at $1.3183, having slipped to a session low of $1.3166 when traders said it broke below stop loss sell orders around $1.3170.
Although analysts partly attributed the euro's drop to year-end dollar demand and thin liquidity, they said unwinding of long euro positions were weighing on the currency.
The euro has made rapid strides since mid-November, gaining around 5 percent in a month to hit an 8-1/2 month high of $1.33085 on Dec. 19 as worries around the euro zone crisis ebbed.
"There is still a good chunk of scepticism among market participants about the euro being significantly higher than the $1.32-$1.33 level," said Ulrich Leuchtmann, head of FX research at Commerzbank.
"Speculative market participants are not very happy with these levels and look at it as a good opportunity to sell the euro which is leading to the rapid drop in euro/dollar."
The euro's falls helped the dollar rise to a two-week high against a basket of currencies, with its index rising to 79.93.
The also reversed earlier gains against the yen to trade down 0.4 percent at 113.51 yen, having earlier hit a 17-month low of 114.675 yen as expectations of more monetary stimulus continued to pressure the Japanese currency.
Commerzbank's Leuchtmann warned the euro would be susceptible to further losses in 2013 if concerns around the Europe's debt crisis re-emerge.
"The long-term assumption that the euro zone crisis is over is a bit shaky and was perhaps overdone. Many of the speculators who increased their long euro positions in the last three months don't have the appetite to carry these long positions into the next year".
Investors were cautious as they waited to see the outcome of a last-chance round of U.S. budget talks, with analysts saying the dollar could benefit from safe-haven buying if no deal is reached by year-end.
U.S. President Barack Obama will meet congressional leaders from both parties on Friday to try to revive talks to avoid tax hikes and spending cuts - together worth $600 billion - that will begin to take effect on Jan. 1.
The dollar was steady against the yen at 86.07 yen, edging away from an earlier peak of 86.64 yen, its strongest since August 2010, when it stopped just shy of reported options barriers at 86.75 yen and 87.00 yen.
Expectations the new Japanese government will push the Bank of Japan to ease monetary policy further has weighed broadly on the Japanese currency and analysts say it could fall further.
The yen's unabated slide, since Shinzo Abe took the helm as Japan's prime minister on Wednesday, has seen it hit fresh two-year lows for three days in succession. Abe has vowed to press for aggressive monetary stimulus to fight deflation.
"Clearly there is some momentum in dollar/yen on expectations the BOJ will become more expansionary and this is currently weighing on the yen," said Marcus Hettinger, global FX strategist at Credit Suisse.
The yen has fallen more than 12 percent against the dollar in 2012, putting it on track for its biggest annual percentage drop since 2005.
The dollar looked set to end the week above its 200-week moving average, now around 84.95 yen, for the first time since late December 2007, a technical signal indicating further gains.