* Dollar strengthens as economic worries persist
* Swiss franc falls from 20-month highs
* Sterling struggles on latest Brexit deal setback
* Graphic: World FX rates in 2019 tmsnrt.rs/2egbfVh (Recasts; adds analyst quote; updates prices; changes ; previous LONDON)
By Kate Duguid
NEW YORK, March 28 (Reuters) - The dollar rose on Thursday against rivals - which were weakened by dovish soundings from central banks - in spite of a cut to the estimate of U.S. economic growth in the fourth quarter.
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 measuring the greenback against a basket of six major currencies gained 0.39 percent to 97.126 , at two-week highs in its third day of gains.
The dollar rally continued in mid-morning U.S. trade even after the Commerce Department announced it had cut its measure of gross domestic product in the fourth quarter, when corporate profits fell by the most in a year. The third reading estimated growth at 2.2 percent, down from the initial estimate of 2.6 percent.
The euro weakened 0.12 percent to $1.1234 as speculation grows that the European Central Bank 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.
"Divergence in economic performance is still a good provider of dollar strength and the evidence is in its favor when it comes to most indicators," said Juan Perez, senior currency trader at Tempus Inc in Washington.
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.
The Swiss franc held near 20-month highs, last at 1.1191 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.
Sterling fell below $1.310 after British Prime Minister Theresa May's offer on Wednesday to quit failed to sway hard-line opponents to back her Brexit withdrawal deal.
Reporting by Kate Duguid and Tommy Wilkes; Editing by Dan Grebler