Parts of the continent are perhaps weeks ahead of the US on the infection curve of the virus, which has killed around 170,000 people worldwide, according to a tally kept by Johns Hopkins University.
The reopenings in the US are a drop in the bucket compared with the more than 22 million Americans thrown out of work by the crisis.
In a dispute that has turned nakedly political, the President has been agitating to restart the economy, singling out Democratic-led states and egging on protesters who feel governors are moving too slowly.
While some states — mostly Republican-led ones - have relaxed restrictions, many governors say they lack the testing supplies they need and warn they could get hit by a second wave of infections, given how people with no symptoms can still spread the disease.
Trump took to Twitter to complain that the "radical left" and "Do Nothing Democrats" are "playing a very dangerous political game" by complaining about a testing shortage. At the same time, Vice-President Mike Pence told governors that Washington is working around-the-clock to help them ramp up testing.
The death toll in the U.S. stood at more than 41,000 — the highest in the world — with over 776,500 confirmed infections, by Johns Hopkins' count. The true figures are believed to be much higher, in part because of limited testing and difficulties in counting the dead.
In other developments:
— Massachusetts has emerged as an alarming hot spot of contagion, with over 1700 dead and officials hoping to bend the curve through aggressive contract tracing.
— New York, with the worst outbreak in the US, reported that hospitalisations in the state have levelled off and the day's death toll, at 478, was the lowest in three weeks, down from a peak of nearly 800. Still, the city cancelled three of biggest events in June: the Puerto Rican Day parade, the Israel parade and the gay pride march.
— A meatpacking plant in Minnesota was shut down after an outbreak there. But Iowa Governor Kim Reynolds refused to order the closing of any slaughterhouses in her state that are seeing alarming increases in Covid-19, saying: "Without them, people's lives and our food supply will be impacted."
Mobilised by the far right, many Americans have taken to the streets in places such as Michigan, Ohio and Virginia, complaining that the shutdowns are destroying their livelihoods and trampling their rights.
But Dr Anthony Fauci, the US Government's top infectious-disease expert, warned on ABC: "Unless we get the virus under control, the real recovery economically is not going to happen."
In the past few days, Florida gave the okay for beaches to reopen, and Texas began a week of slow reopenings, starting off with state parks; later in the week, stores will be allowed to offer curbside service. Both states are led by Republicans.
Boeing's shutdown went into effect March 25 after workers tested positive for the virus and an inspector for the company died. Washington was the first state to see a spike in Covid-19 cases and enacted strict shutdown orders that helped tamp the virus down.
Businesses that start operating again are likely to engender good will with the Trump administration at a time when it is doling out billions in relief to companies.
Detroit's major automakers suspended operations a month ago but are negotiating with union leaders in hopes of reopening in May. Some operations are being converted to build ventilators.
Even with the outbreak easing in places, the head of the World Health Organisation, Tedros Adhanom Ghebreyesus, cautioned, "The worst is yet ahead of us."
He did not specify why he believes so. But there are signs the virus is swelling in Africa, where the health care system is in poor shape.
In Europe, cars are about to begin rolling off some assembly lines in Germany, Sweden and Slovakia.
In Australia, the country's longest-running soap opera, Neighbours, planned to restart shooting, and one city reopened beaches for exercise like swimming, running and surfing, but not for sunbathing.
"Living along the coast, I know how important our beaches are to the mental and physical health of so many," said Danny Said, Mayor of Randwick.
Hair salons, dentists, physical therapists and tattoo parlors were allowed to reopen in Denmark, but it was not business as usual.
Christel Lerche sprayed chairs with alcohol at her salon in suburban Copenhagen and provided hand sanitiser and plastic coat hangers — to be cleaned after each use — to customers keen to get their hair styled for the first time in over a month. No magazines were left for customers to share.
India eased the world's largest lockdown to allow some manufacturing and agricultural activity to resume. Iran began opening intercity highways and major shopping centres.
In Italy, tensions have been growing between northern regions, which are pushing to reopen industry despite being hit hardest by the virus, and the south, which fears contagion if the lockdown is eased. Premier Giuseppe Conte is expected to outline this week what the next phase may look like.
Still, Gucci restarted some workshops for leather accessories and shoes.
In Britain, where Prime Minister Boris Johnson is still recovering from a bout of Covid-19 that put him in intensive care, authorities have cautioned that the lockdown is unlikely to be significantly loosened in the short term.
France also is still under a tight lockdown, although starting today, authorities allowed families, under strict conditions, to visit relatives in nursing homes once again.
- AP