* Mnuchin says weak dollar is good for U.S. trade
* Dollar index hits fresh 3-year low (Updates prices, market activity, adds comment)
NEW YORK, Jan 24 (Reuters) - The dollar slumped to a fresh three-year low against a basket of major currencies on Wednesday after the U.S. Treasury secretary said he welcomed a weaker greenback, and as investors worried about U.S. President Donald Trump's protectionist agenda.
Speaking at the World Economic Forum in Davos on the eve of Trump's arrival at the Swiss resort, Treasury Secretary Steven Mnuchin said the weaker dollar was positive for U.S. trade.
"It's quite significant given that this is the first time in a very long time that a Treasury secretary has spoken against a strong dollar," said Sireen Harajli, FX strategist at Mizuho.
Mnuchin's comments provided a fresh trigger for dollar selling and raised questions about whether a weaker U.S. currency could provide a long-term impetus for the economy.
Dollar bears were also emboldened by Trump's executive order imposing steep import tariffs on washing machines and solar panels, a move condemned by China and South Korea, analysts said.
"Any time we have these types of trade frictions it's going to put more negative sentiment on the currency," said Minh Trang, senior currency trader at Silicon Valley Bank in Santa Clara, California.
The dollar index, which measures the greenback against a basket of six major currencies, was down 0.99 at 89.235, slipping below 90 for the first time since December 2014. The dollar was down about 1 percent against the yen .
The dollar is very stable and Trump believes in a free-floating currency, the White House said on Wednesday.
The dollar has been pressured for months by the view that the Federal Reserve is no longer the only central bank seeking to tighten monetary policy as growth in other regions, Europe in particular, picks up speed.
The euro was up 0.84 percent against the greenback. Euro zone businesses kicked off 2018 at a better-then-expected pace, ramping up activity at the fastest rate since mid-2006, a survey showed.
Investors awaited the European Central Bank's meeting on Thursday for any signals that policymakers are becoming concerned with the recent rally in the euro.
"I would expect the commentary to be quite careful around the currency impacts," said Bill Northey, senior vice president, U.S Bank Wealth Management in Helena, Montana.
A stronger euro has implications for export capabilities, growth of the economy and inflationary targets that the ECB hopes to achieve, Northey said.
Sterling jumped above $1.42 as strong British employment data and broad-based dollar weakness prompted investors to ramp up long positions in the pound. (Reporting by Saqib Iqbal Ahmed; Additional reporting by Karen Brettell; Editing by Meredith Mazzilli and Richard Chang)