* 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)
By Tommy Wilkes
LONDON, March 28 (Reuters) - The dollar rose on Thursday as other currencies struggled, following more dovish soundings from central banks and renewed expectations that the European Central Bank will keep rates low for longer.
The Reserve Bank of New Zealand this week joined a growing list of central banks that have turned dovish amid signs of a slowing global economy, saying 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 0.4 percent to 97.155, its third day of gains and its best level since March 12.
The euro weakened 0.2 percent to $1.1225 as speculation grows that the ECB will introduce a tiered deposit rate - a sign that policymakers plan to keep interest rates low for longer. The euro remains above 21-month lows of $1.1167 touched a few weeks ago.
Tumbling euro zone government bond yields have also weighed on 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 held near 20-month highs of 1.1186 francs per euro. Analysts noted that the Swiss National Bank has intervened below 1.12 in the past to stop the franc from strengthening further.
The New Zealand and Australian dollars recovered somewhat after the New Zealand central bank's dovish shift knocked 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 0.1 percent to 110.38 to the dollar as Japanese shares fell, but it was some distance from Monday's six-week high of 109.70.
Risk aversion 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