Spain, Nigeria, Azerbaijan, Malaysia, Israel, Tunisia and Lebanon were also among countries lightening some restrictions, reopening factories, building sites, parks, hairdressers and libraries in various ways. Over the weekend around half of states in the United States partially reopened their economies.
The easing comes as the daily rate of new COVID-19 cases worldwide has sat down from a peak of around 13 percent in mid-March in a 2 percent -3 percent range over the last week.
According to a Reuters tally based on government data, global cases have climbed to around 3.52 million. However, cases can only cause mild symptoms and not everybody with symptoms is tested, while most countries only record deaths in hospitals.
"We still need to be skeptical about the numbers we get," Peter Collignon, a physician and microbiologist at Canberra Hospital for infectious diseases, told Reuters.
"We could easily have a second or a third wave because many places are not immune," said Collignon, noting the world was well short of herd immunity, which requires about 60 per cent of the population to recover from the disease.
Countries are only reopening gradually because of these fears.
In Italy, where nearly 29,000 people have been killed by the novel coronavirus, factories can restart dormant production lines, parks can reopen while relatives can meet up again.
Friends were told to keep apart, however, and most shops have to remain shut until May 18. Restaurants and bars can only offer take-aways, while for the indefinite future schools, cinemas, and theatres will remain shut.
"It's good to be back, but the world has completely changed," Gianluca Martucci said, pulling up the shutters at a catering company's small warehouse in Rome's backstreets.
"So far, the government was very wise, but I'm worried we could start a little too soon ... I don't know if a second wave could survive in that country.
A phased reopening like that of Italy, with local variations, is also being pursued elsewhere.
Israel has begun relaxing the curbs after weeks of strict closures. Children's schools in grades 1-3, aged six to nine, reopened in late April, following the opening of some shops.
If this plan is approved by the cabinet on Monday, hotels, gyms, swimming pools, libraries, museums, non-medical treatments and grade 4-6 school would reopen on 17 May. If infection rates remain low, on May 31 restaurants, cinemas, event halls and grades 7-10 in school would follow.
A first stage of reopening began in Tunisia on Monday, with half of the civil service returning to work as well as building sites and public transport.
For at least a week, clothing and furniture shops, hairdressers and carpentry workshops are not supposed to reopen, but some have already started welcoming in customers.
"I am happy that my business is back," said Salma ben Naceur, owner of a furniture shop in Tunis' Mnihla suburb. "We'd declared bankruptcy if the suspension continued for another month."
WAR OF WORDS ON VIRUS
Officials go to the lengths to stress that lightening measures does not mean that people should lower their guard.
Italian Prime Minister Giuseppe Conte said that the country was still in the "full throes of the pandemic," saying to La Stampa newspaper that "phase 2" of the lockdown should not be seen as a signal that we are all free.
In the United States, even as warm weather led sunseekers to flock into Manhattan's green spaces, the epicenter of the U.S. epidemic, President Donald Trump warned that the death toll could rise to 100,000 nationwide. Already almost 68,000 have been killed by the coronavirus.
Governments are reluctant to prolong draconian measures which have come at a high economic price, although often broadly backed by the public.
In April, business surveys showed that factory activity was ravaged around the world and the outlook looked bleak as shutdowns froze global production and slashed demand. As a result, this year's global economy is expected to suffer its steepest recorded contraction.
"This past week saw the amazing coincidence of the Western world's deepest quarterly economic decline in nearly 100 years, and the conclusion of the strongest monthly equity rally in more than 30 years," said Erik Nielsen, UniCredit's chief economist.
As investors around the world feared a new trade war, escalating tensions between the United States and China over the origin of the pandemic drove down stock markets and oil prices Monday.
A.S. State Secretary Mike Pompeo said there was "a significant amount of evidence" on Sunday that the virus had emerged from a laboratory in Wuhan, a Chinese town. He has not provided evidence or disputed an earlier conclusion of U.S. intelligence that the virus was not man-made.
An editorial in China's Global Times said he was "bluffing" and called on the U.S. to give evidence.