* Risk rally runs out of steam, commodity currencies fall most
* Kiwi jumps as lockdown rules to ease
* Graphic: World FX rates in 2020 https://tmsnrt.rs/2RBWI5E
By Tom Westbrook
SINGAPORE, April 20 (Reuters) - The dollar found support on Monday as global growth fears hit oil prices and commodity currencies, while the New Zealand dollar rose on news that the government will begin to relax strict virus containment measures from next week.
The oil-sensitive Canadian dollar CAD=D3 , Russian rouble RUB= and Norwegian krone NOK= each dropped about 0.5% as weak demand and a supply glut crushed U.S. crude prices to a 21-year low. O/R
The dour mood weighed on riskier Asian currencies and pushed the Australian dollar a touch lower. But the kiwi jumped 0.5% after New Zealand Prime Minister Jacinda Ardern said a gradual roll back of lockdown rules would begin on April 27. nation, which has recorded just 12 deaths from COVID-19, the respiratory disease caused by the new coronavirus, will lower its alert level one notch next Monday - allowing some businesses to resume - and review that stance on May 11.
"The market wasn't expecting quite such a short timeframe for the potential relaxation of restriction levels," said Ray Attrill, head of FX at National Australia Bank in Sydney.
"However the risk sentiment today is not quite as positive as it was," he said. "There is still a degree of safe haven support and a level of demand for U.S. dollar that is going to transcend whether or not we are in risk-on or risk-off mode."
The Australian dollar AUD=D3 sat at $0.6354, about 1.5% below a month-high hit last week, while the kiwi NZD=D3 hit a three-session high of $0.6059.
Moves in other majors were modest, but together with cautious trade in regional equities markets seemed to cap a few weeks of risk appetite and dollar softness.
The dollar was a tad firmer on other majors, gaining about 0.1% on the euro and pound and 0.3% on the Japanese yen. It last bought 107.80 yen JPY= and traded at $1.2478 per pound GBP= and $1.0870 per euro EUR= .
'EYE OF THE STORM'
New Zealand's move to ease its tough lockdown comes as the country has all but halted the virus' spread - it has one of the lowest per-capita case counts in the world and has traced all but eight of 1,440 national cases to its source.
The relaxation is only modest, allowing for the resumption of construction, forestry and manufacturing and not socialising, but Ardern said further easing would be considered next month.
The picture elsewhere, though, is less clear and is joined by a wave of economic destruction.
An almost 12% drop in Japan's exports in March reported on Monday, the steepest slump in nearly four years, augurs badly. the United States, where the death toll rose to more than 40,000 on Sunday, state governors have sparred with President Donald Trump over virus testing capacity and how quickly their economies can re-open. is not considering lifting its lockdown, a senior minister said on Sunday, while leaders in Ireland and Canada have flagged long-lasting social distancing rules. are coming into the eye of the storm," said Chris Weston, head of research at brokerage Pepperstone in Melbourne.
"And as the market starts to focus less on virus headlines, or at least will be less sensitive to better news, we will focus more on the lasting effects on the economy and solvency."
Elsewhere China's yuan CNY= eased after a cut to a benchmark interest rate and the Mexican peso MXN= dropped about 1% following Moody's downgrading the sovereign credit rating on Friday.