* Dollar strengthens as economic worries persist
* Swiss franc falls from 20-month highs; Yen supported
* Sterling struggles on latest Brexit deal setback
* Graphic: World FX rates in 2019 tmsnrt.rs/2egbfVh (Adds details, quote, graphic, updates prices)
By Tommy Wilkes
LONDON, March 28 (Reuters) - The dollar rose on Thursday as rival currencies struggled following more dovish soundings from central banks, while the yen gained as investor worries about the global economy grew.
The Reserve Bank of New Zealand joined a growing list of central banks that have turned dovish amid signs of a slowing global economy, saying on Wednesday its next move in interest rates was likely to be a cut.
With many currencies on the defensive, the dollar has brushed aside a decline in benchmark U.S. Treasury yields to 15-month lows. The dollar index against a basket of six major currencies gained 0.2 percent to 96.974 and headed for its third day of gains.
The euro held around $1.1255, away from 21-month lows of $1.1167 touched a few weeks ago.
It has lost nearly half a percent this week as the benchmark 10-year German bund yield fell to a 2 1/2-year low. Dovish comments from ECB President Mario Draghi on Wednesday did little to support the euro.
"The market is becoming more concerned about global growth conditions, especially to the detriment of the euro zone. The dollar strength is on the back of other currencies getting hurt," said Manuel Oliveri, FX analyst at Credit Agricole.
However, Oliveri said that he did not advise chasing the euro much lower because of the "low bar" for the euro zone economy to surprise on the upside.
The Swiss franc slipped from 20-month highs hit on Wednesday, falling 0.2 percent against the euro to 1.1204 francs . Analysts noted that levels below 1.12 have in the past prompted intervention by the Swiss National Bank to stop the franc from further strengthening.
The New Zealand and Australian dollars managed to recover somewhat after the New Zealand central bank's dovish shift hit both currencies lower on Wednesday.
Growth-sensitive currencies have taken a beating recently on rising risks to the global economy.
Analysts at ING said investors had gone too far in expecting a U.S. rate cut this year, but that the dollar remained vulnerable for now.
"For the short term, however, DXY looks vulnerable to the massive erosion in USD yield differentials and could easily head back to 96," they wrote.
The yen rallied 0.2 percent to 110.33 to the dollar as Japanese shares fell, but it was some distance from Monday's six-week high of 109.70.
Broader risk aversion in markets also supported demand for the yen, which is considered a safer place to park cash in times of uncertainty.
Sterling fell towards $1.31 after British Prime Minister Theresa May's offer on Wednesday to quit failed to sway hard-line opponents to back her Brexit withdrawal deal.
Editing by Larry King and Susan Fenton