* Euro falls vs firmer dollar as risk appetite fades
* Euro/yen pulls away from previous day's 18-month high
* Dollar/yen pauses after hitting 29-month peak
By Anooja Debnath
LONDON, Jan 3 (Reuters) - The dollar hit a three-week high against a basket of currencies while the euro plumbed its lowest level since mid-December on concerns that further U.S. budget wrangling could lie ahead.
Initial optimism about a deal to avoid steep U.S. tax rises and spending cuts late on Tuesday pushed down the dollar, particularly against riskier and growth-linked currencies. But the euphoria quickly faded as worries about future budget talks re-emerged.
This gave the U.S. currency a lift, taking the dollar index as high as 80.229, its strongest since Dec. 11. The dollar is often favoured at times of market uncertainty and strategists said it could see further gains in coming weeks.
"The reality is that budget talks will continue for the next two months and could get sour," said Jane Foley, senior currency strategist at Rabobank. "There could be a messy two months ahead and we see the dollar index reclaiming some ground."
The dollar's rise pushed the euro down 0.7 percent to a three-week low of $1.3082 after stop-loss sell orders were triggered below $1.3090, traders said. This took the euro well below a peak around $1.3300 hit on Wednesday.
Highlighting market concerns that the deal left key U.S. deficit issues unresolved, ratings agency Moody's Investors Service said the United States needed to do more to protect its Aaa debt rating.
Strategists also said the current weakness in the euro could persist due to the weak fundamentals in the euro zone, on any fresh debt concerns in the currency bloc and increasing prospects of an interest rate cut by the European Central Bank.
The euro fell more than 1 percent on the day to 113.65 yen as investors took profits on its rise to an 18-month high of 115.995 yen hit 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 low-yielding yen, which fell on Wednesday in the wake of the U.S. deal, recovered against the dollar but remained near a 29-month low and looked fragile on expectations the Bank of Japan will ease monetary policy further.
The dollar was down 0.6 percent at 86.82 yen after rising as high as 87.36 yen earlier on Thursday on trading platform EBS, its highest since late 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 BOJ into further monetary easing to beat deflation.
But Mizuho's Asher said that although the dollar could extend its gains against the yen it would not "go in a straight line all the way up to 90 yen".
"There has to be some pull-backs and periods when people think it is over-stretched."
The yen is likely to remain vulnerable until the BOJ's policy meeting on Jan. 21-22.