Venice geared up to receive tourists, Milan's pizzerias prepared for hungry customers and Australians went out to eat for the first time in weeks Saturday, but the reopening of restaurants, pubs and cafes came with a warning: Don't overdo it.

Public health experts urged caution as governments eased restrictions on eateries, shops and parks in many countries and rolled out measures to restart dormant factories. The coronavirus pandemic, which has killed more than 300,000 people, has slowed in many places but could pick up again if precautions are not taken or officials move too quickly to get people back to work.

"The message is, yes, appreciate all the efforts, appreciate the opportunity to release some of those measures, but let’s not have a party, let’s not go to town," said Tony Bartone, president of the Australian Medical Association.

Most restaurants are limited to 10 customers at a time, and Bartone said people must maintain social distance, follow coughing etiquette, wash their hands regularly and stay away from others if they are ill.

In New Zealand, even Prime Minister Jacinda Ardern and her fiance, Clarke Gayford, were initially turned away for Saturday brunch by a restaurant in the capital city, Wellington, because it was too full under coronavirus guidelines.

There was a happy ending: A spot freed up, and staff chased down the street to call the couple back.

Italy’s tourism industry is focused firmly on June 3, when both regional and international borders reopen, allowing the first prospect of tourists since Europe’s first lockdown went into place in early March. In tourist-reliant Venice, occupancy of the city’s 50,000 hotel beds has hovered around zero ever since.

"Venice lives on tourism, period,’’ said Claudio Scarpa, head of the city’s hotel association. ’’All the economic structures that operate in the city, including the port, are tied to tourism."

While Venice hopes for some kind of restart, it may have to wait a while yet. Germany - its border about a four-hour drive from Venice - is instructing citizens not to travel abroad for tourism until at least June 15.

France was also being cautious, calling for a coordinated European effort on opening. At the same time, French officials could make decisions "that protect the French" regarding countries "where the virus is still active," Interior Minister Christophe Castaner said Saturday.

As hundreds of French beaches reopened, Castaner warned that the government would not hesitate to close them again if rules are not respected, including a ban on sunbathing.

Local authorities were charged with deciding which beaches would reopen as part of a staggered plan to end a strict two-month lockdown that began March 17. Under the rules, beachgoers can take a dip but cannot lay in the sun or picnic in the sand. Social distancing rules must be maintained, and groups must be limited to 10 people.

"The virus is still there," Castaner said. "It moves around with our movements"

In Milan, Italy's financial capital, 3,400 restaurants planned to open Monday, along with 4,800 bars, 2,900 hairdressers, 2,200 clothing stores and 700 shoe shops.

"After a long period at home, we will all want to go out and have a good coffee in a bar, eat a pizza in a pizzeria, buy a pair of jeans, or go to the hairdressers," Milan Mayor Giuseppe Sala said Saturday in a Facebook video.

Many restaurant owners complained that the new rules for reopening were unclear and that the entire sector - including suppliers and food producers - was suffering. Dozens protested outside Milan's main train station and called for an abolition of taxes and more help.

In Britain, officials and tourism boards discouraged people from visiting popular tourist spots - like beaches or country parks - on the first weekend since lockdown rules were eased in England. Stricter rules remain place in other parts of the U.K., and English daytrippers have been warned against crossing into Scotland or Wales.

In Spain, Prime Minister Pedro S?nchez said he would ask Parliament for what he hopes will be the last extension of the country’s state of emergency to battle the coronavirus pandemic, until around late June.

Spain is slowly scaling back confinement measures, but the tourism industry, which accounts for 12 percent of GDP, looks set to lose its critical summer season.

"Spain needs tourism, but tourism needs security. It needs health guarantees," S?nchez said Saturday.

In the United States, an Associated Press analysis found that 41 of the nation's 50 states fall short of the COVID-19 testing levels that experts say are necessary to avoid another wave of outbreaks, even as some of those states move aggressively to allow businesses to reopen.

Rapid, widespread testing is considered essential to tracking and containing the coronavirus. The AP analysis was based on metrics developed by Harvard University’s Global Health Institute.

Harvard researchers have calculated that the U.S. needs to test at least 900,000 people daily to reopen the economy safely, nearly three times the current tally of about 360,000, according to figures compiled by the COVID Tracking Project website.

In the South, New Orleans took its first steps Saturday to loosen restrictions that have been in place for two months.

The rest of Louisiana took that step Friday as many businesses and houses of worship were allowed to reopen at 25 percent capacity. New Orleans is slightly more restrictive. In addition to the 25 percent capacity restrictions, restaurants and certain other businesses such as nail salons are required to take reservations. The city has also imposed caps designed to keep houses of worship and movie theaters at fewer than 100 people. Casinos, video poker, live entertainment and bars are still closed.

Some restaurateurs in the city famous for its cuisine decided to try reopening. Others planned to stick to takeout or stay closed all together.

Kirk Estopinal, one of the owners of Cane & Table in the French Quarter, said the restaurant will open Saturday. Guests can order their food when they make a reservation online and are asked to wear masks. Cleaning will be stepped up, and bathrooms cleaned after every use.

"We’re going to trial run what it is to operate in the new normal," he said. "We’re looking at a restaurant experience that is almost touch-less for our guests."

In South Korea, which has one of the highest levels of virus testing, a Health Ministry spokesman said Saturday that the country may have dodged a major outbreak after finding 162 cases linked to nightclubs in Seoul, the densely populated capital.

Son Young-rae said 46,000 people have been tested in the club-related outbreak.

India overtook China in the number of confirmed infections as Prime Minister Narendra Modi’s government was due to announce this weekend a decision whether to extend the 54-day-old lockdown. India counted almost 86,000 infections and more than 2,700 deaths, compared with China's nearly 83,000 confirmed case and more than 4,600 fatalities.

China plans to shorten its annual legislative session next week in Beijing as small clusters of infections pop up elsewhere in the country. The spread of the disease has largely stopped in the country where the pandemic started, but Jilin province in the northeast has reported 28 cases over nine days, the latest two on Friday.