(Adds quote from Chinese ambassador to UN, U.S. stocks move)
* China reports big fall in new cases at centre of epidemic
* Global death toll rises above 3,000; over 86,500 infected
* Stock markets and oil rebound on hopes of government action
* Graphic: Tracking the coronavirus here
By Stephanie Nebehay and Se Young Lee
GENEVA/BEIJING, March 2 (Reuters) - The new coronavirus now appears to be spreading much more rapidly outside China than within but can still be contained, and stigma is more dangerous than the disease itself, the World Health Organization said on Monday.
WHO chief Tedros Adhanom Ghebreyesus said almost eight times as many cases had been reported outside China as inside in the previous 24 hours, adding that the risk of coronavirus spreading was now very high at a global level.
He said outbreaks in South Korea, Italy, Iran and Japan were the greatest concern, but that there was evidence that close surveillance was working in South Korea, the worst affected country outside China, and the epidemic could be contained there.
"Stigma, to be honest, is more dangerous than the virus itself. Let's really underline that. Stigma is the most dangerous enemy," he told a news briefing in Geneva.
He said the fight against the coronavirus should become a bridge for peace, commending the United States for supporting sending medical aid to Iran despite the tensions between them.
"I think we have a common enemy now," he said.
The global death toll exceeded 3,000, with the number of dead in Italy jumping by 18 to 52. Latvia, Saudi Arabia, Senegal and Morocco reported cases for the first time, bringing the total to more than 60 countries with the illness known as COVID-19.
But equity markets surged after their worst plunge since the financial 2008 crisis last week, encouraged by the prospect of government action to stem the economic impact. In the United States, the Dow jumped nearly 1,300 points, or 5%, while the S&P 500 closed 4.6% higher.
Finance ministers of the G7 group of leading industrialised democracies were expected to discuss measures in a conference call on Tuesday, sources told Reuters.
Oil prices jumped 4% amid hopes of a deeper output cut by the Organization of the Petroleum Exporting Countries (OPEC).
(Graphic: Tracking the coronavirus here)
A senior U.S. official said he was concerned about a likely jump in the number of cases in the United States, which has had more than 90, with six deaths.
"When you have a number of cases that you've identified and they've been in the community for a while, you're going to wind up seeing a lot more cases than you would have predicted," Dr Anthony Fauci, head of the infectious diseases unit at the U.S. National Institutes of Health, told CNN.
South Korea has had 26 deaths and reported another 599 infections on Monday, taking its tally to 4,335.
Of the new cases in South Korea, 377 were from the city of Daegu. That is home to a branch of the Shincheonji Church of Jesus, to which most of South Korea's cases have been traced after some members visited the Chinese city of Wuhan, where the disease emerged.
The Seoul government asked prosecutors to launch a murder investigation into leaders of the church. Seoul Mayor Park Won-soon said that if founder Lee Man-hee and other heads of the church had cooperated, fatalities could have been prevented.
Lee knelt and apologised to the country, saying that one church member had infected many others and calling the epidemic a "great calamity". "We did our best but were not able to stop the spread of the virus," Lee told reporters.
It was not immediately known how many of South Korea's dead were members of the church.
But Wuhan itself, at the centre of the epidemic, shut the first of 16 specially built hospitals that were hurriedly put up to treat coronavirus cases, the Chinese state broadcaster CCTV said.
There was also a steep fall in new cases in Hubei, the province around Wuhan, but China remained on alert for people returning home with the virus from other countries.
The virus broke out in Wuhan late last year and has since infected more than 86,500 people, mostly in China.
Only eight cases were reported in China beyond Hubei on Sunday, the WHO said.
China's U.N. Ambassador Zhang Jun, at a news conference at the United Nations to mark China's presidency of the Security Council for March, said: “We definitely believe that with the coming of spring we’re not far from the coming of the victory of the final defeat of COVID-19.”
Outside China, there are now more than 8,700 infected and over 125 deaths.
Iran, one of the worst-hit nations, reported infections rising to 1,501, with 66 deaths, including a senior official. With stocks of gloves and other medical supplies running low in pharmacies, authorities uncovered a hoard of supplies including millions of gloves.
In Britain, which has 40 confirmed cases, Prime Minister Boris Johnson urged people to be prepared for a further spread.
Factories worldwide took a beating in February from the outbreak, with activity in China shrinking at a record pace, surveys showed, raising the prospect of a coordinated policy response by central banks.
The epidemic has forced the postponement of festivals, exhibitions, trade fairs and sports events and damaged tourism, retail sales and global supply chains, especially in China, the world's second-largest economy.
An official of the International Air Transport Association (IATA) said airlines stood to lose $1.5 billion this year due to the virus and urged governments to help them.
The Organization for Economic Cooperation and Development warned that the outbreak was pitching the world economy into its worst downturn since the global financial crisis, urging governments and central banks to fight back.
(For more coverage of the coronavirus, see here)
Reporting by Stephanie Nebehay in Geneva, Hyonhee Shin and Jack Kim in Seoul, Ju-min Park in Gapyeong, Ryan Woo, David Stanway, Se Young Lee, Emily Chow and Andrew Galbraith in Beijing, Leigh Thomas in Paris, Michelle Price in Washington, Leika Kihara in Tokyo, Jonathan Cable in London, Donny Kwok and Twinnie Siu in Hong Kong and Grant McCool in Washington; writing by Nick Macfie, Philippa Fletcher and Lisa Shumaker; editing by Mark Heinrich, Kevin Liffey and Bill Berkrot