Spain and Austria have allowed partial returns to work while Britain, France and India extended lockdowns to rein in the coronavirus and the United States - where the death toll exceeded 25,000 - debated how to reopen its economy.
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The World Health Organisation (WHO) warned that infections had "certainly" not yet peaked.
Nearly 2 million people globally have been infected and more than 124,000 have died in the most serious pandemic in a century, according to a Reuters tally.
The epicentre has shifted from China, where the virus emerged in December, to the United States, which has now recorded the most deaths.
World leaders, in considering easing curbs, have to balance risks to health and to the economy as the lockdowns have strangled supply lines, especially in China, and brought economic activity to a virtual halt.
The shutdown is costing the US economy perhaps $US25 billion ($A39 billion) a day in lost output, St Louis Federal Reserve President James Bullard said, calling for widespread testing and risk management strategies so the economy can restart.
US President Donald Trump, who has declared he will decide when to lift lockdowns, suggested some Democratic state governors were "mutineers" after New York Governor Andrew Cuomo said he would refuse any order that risked reigniting the outbreak.
The White House said Trump would hold a video teleconference with leaders from the Group of Seven countries on Thursday to co-ordinate responses.
The global economy is expected to shrink by 3.0 per cent this year, the International Monetary Fund said, marking the steepest downturn since the Great Depression.
The WHO said the number of new cases was tailing off in some parts of Europe, including Italy and Spain, but outbreaks were growing in Britain and Turkey.
"The overall world outbreak - 90 percent of cases are coming from Europe and the United States of America. So we are certainly not seeing the peak yet," WHO spokeswoman Margaret Harris told a briefing in Geneva.
But world stocks gained after Chinese trade data came in better than expected and as some countries partly lifted restrictions.
Some Spanish businesses, including construction and manufacturing, were allowed to resume. Shops, bars and public spaces are to stay closed until at least April 26.
Spain was flattening the curve on the graph representing the rate of growth of the outbreak, Health Minister Salvador Illa said on Tuesday. The overnight death toll from the coronavirus rose to 567 on Tuesday from 517 a day earlier, but the country reported its lowest increase in new cases since March 18. Total deaths climbed to 18,056.
Italy, which has the world's second highest death toll at 21,067, maintained some tight restrictions on movement, while Denmark, one of the first European countries to shut down, will reopen day care centres and schools for children in first to fifth grade on April 15.
The Czech government will gradually reopen stores and restaurants from April 20, although people will continue to be required to wear masks.
Thousands of shops across Austria reopened on Tuesday, but the government cautioned that the country was "not out of the woods".
Austria acted early to shut schools, bars, theatres, restaurants, non-essential shops and other gathering places about four weeks ago. It has told the public to stay home.
The Alpine republic has reported 384 deaths in total, fewer than some larger European countries have been suffering each day. Hospitalisations have stabilised.
Britain, where the government has come under criticism for its slow approach to testing and for not getting protective equipment to the frontlines of health care, has the fifth-highest death toll globally.
The toll in British hospitals rose to 12,107 as of Monday but is expected to be much higher when deaths in the community are included.
Foreign Secretary Dominic Raab has said there would be no easing of lockdown measures when they come up for review this week.
The Times newspaper said on Tuesday that Raab, deputising for Prime Minister Boris Johnson who is recuperating from a COVID-19 infection, would extend the curbs until at least May 7.
In France, President Emmanuel Macron on Monday extended a virtual lockdown to May 11.
India, the world's second-most populous country after China, extended its lockdown until May 3 as the number of coronavirus cases crossed 10,000. Neighbours Pakistan and Nepal also extended their curbs.
Australian Associated Press