* Dollar buoyant on strong US manufacturing, construction data
* Fed minutes also support dollar, seen as hawkish
* Dollar index pulls further away from 3-1/2-month low
* Greenback gains against safe-havens as risk assets rally
TOKYO, Jan 4 (Reuters) - The dollar extended gains on Thursday after upbeat U.S. data and supportive minutes from the Federal's Reserve's latest policy meeting helped it shake off recent weakness.
The dollar was 0.2 percent higher at 112.710 yen in early Asian trading. It touched a 2-1/2-week low of 112.055 on Tuesday after declining steadily from a high above 113.750 scaled in December.
The euro was 0.05 percent lower at $1.2011 after losing roughly 0.4 percent overnight. The common currency had surged to a three-month high of $1.2081 on Tuesday.
The dollar bounced after Wednesday's strong U.S. manufacturing and construction data.
It gained further support as the minutes from the Fed's Dec. 12-13 meeting were seen as more hawkish than anticipated, indicating the central bank is still poised to raise interest rates several times this year.
Fed policymakers acknowledged the U.S. labor market's solid gains and the expansion in economic activity, even as they affirmed policymakers' worries about persistently low inflation.
That suggested the central bank will continue to pursue a gradual approach in raising rates but could pick up the pace if inflation accelerates.
"The dollar did feel downward pressure at the turn of the year, but the selling was not based on very strong factors," said Masafumi Yamamoto, chief currency strategist at Mizuho Securities in Tokyo.
Rebalancing of positions caused by investors closing their books towards the turn of each year can lead to dollar selling.
"As such, strong U.S. data and the Fed's minutes, which suggested board members were not as pessimistic towards the potential economic impact of U.S. tax cuts as many in the market expected, helped the dollar get back on course," Yamamoto said.
Increasing investor risk appetite in broader markets also supported the dollar, notably against perceived safe-havens like the yen and Swiss franc, which was at 0.9776 franc per dollar after sliding 0.6 percent the previous day to pull back from a three-month peak of 0.9699.
Buoyed by overnight gains on Wall Street, Tokyo's Nikkei began the first day of trading in 2018 by rallying more than 2 percent. Crude oil prices were at 2-1/2-year highs, helping fuel inflation expectations.
The pound dipped 0.1 percent to $1.3510, following overnight losses of 0.6 percent, when it fell back from a 3-1/2-month high of $1.3614 overnight against a rebounding dollar.
The Australian dollar slipped 0.2 percent to $0.7822 and the New Zealand dollar dipped 0.1 percent to $0.7085.
The dollar index against a basket of six major currencies extended the previous day's bounce to stand 0.1 percent higher at 92.248. It had declined to 91.751 on Tuesday, its lowest since Sep. 20. (Reporting by Shinichi Saoshiro; editing by Richard Pullin)