The EU has offered “a heartfelt apology” to Italy for letting it down at the start of the coronavirus crisis as fresh evidence emerged that few European countries are likely to have achieved herd immunity as they begin cautiously lifting their lockdowns.

As the World Health Organization warned that the continent remained firmly “in the eye of the storm”, the president of the European commission said on Thursday that truth was needed to overcome the Covid-19 pandemic – including political honesty.

“Too many were not there on time when Italy needed a helping hand at the very beginning,” Ursula von der Leyen told the European parliament. “And yes, for that it is right that Europe as a whole offers a heartfelt apology.”

Early in the crisis, both France and Germany imposed export bans on vital medical equipment, while no EU country initially responded to Italy’s call for aid via the bloc’s emergency mechanism. While healthcare policy and provision is the responsibility of member states, the EU is meant to support cooperation between them.

Play Video 8:07 How coronavirus changed the world in three months – video

An opinion poll last month found that 88% of Italians felt the EU was failing to support their country, prompting fears in Brussels and other national capitals of a Eurosceptic backlash. Von der Leyen’s direct apology went further than a previous statement in which she she chided member states for their “only-for-me response”.

As more European governments begin easing physical distancing restrictions, a Dutch study suggested only a tiny percentage of people may have developed antibodies against Covid-19, reinforcing concerns about a “second wave” of infections when populations embark on a gradual return to normal life.

Jaap van Dissel of the National Institute for Public Health (RIVM) said the study of more than 7,000 Dutch blood donors found just 3% had developed antibodies against the virus. The figure suggested only “several hundred thousand people” were likely to have contracted Covid-19 in a country of 17 million, he said.

The study followed a similar survey of 1,500 people in Austria who were not in hospital during early April. That found that less than 1% of the population was “acutely infected” with the virus.

The WHO’s regional director for Europe, Hans Kluge, cautioned on Thursday that despite “optimistic signs” in some of the countries worst hit by the virus, such as Italy and Spain, the number of global cases was still rising – and half were in Europe.

While new infections were broadly declining in Spain, Italy, Germany, France and Switzerland, sustained or increasing levels were still being recorded in Britain, Turkey, Ukraine, Belarus and Russia, Kluge said, urging countries that had started easing restrictions to make sure control mechanisms were in place.

“It is imperative we do not let down our guard,” Kluge said. Countries should ensure transmission was under control before they began lifting lockdowns, and that their healthcare systems had the capacity “to identify, isolate, test, trace and quarantine”.

Workplaces needed to take preventative measures, and countries needed to effectively manage the risks of importing new cases from abroad, he added. If governments cannot meet all these criteria, Kluge said, they should “please rethink”.

Denmark on Wednesday became the first country in Europe to start reopening its schools, while Austria, Italy and Spain have allowed certain businesses to reopen and some non-essential workers to go back to their jobs.

Germany has announced initial steps to reopen some shops and gradually restart schools from 4 May, while French pupils will begin returning to school from 11 May. Finland has lifted a travel blockade on the Helsinki region.

Typical of countries further advanced along the pandemic curve, Spain, which has recorded 19,130 deaths, on Thursday announced 5,183 new cases – a rise of 2.9% over the previous 24 hours, well down from the daily average of 12% at the end of March and 20% in mid-March.

Von der Leyen said of letting Italy down at the beginning of the pandemic: “Yes, it is true that no one was really ready for this,” she told the European parliament.

“It is also true that too many were not there on time when Italy needed a helping hand at the very beginning. And yes, for that, it is right that Europe as a whole offers a heartfelt apology.” More than 21,000 people have died from the virus in Italy, the highest death toll in Europe.

Facebook Twitter Pinterest Ursula von der Leyen: ‘It is right that Europe as a whole offers a heartfelt apology.’ Photograph: Thierry Monasse/Getty Images

According to the Johns Hopkins University tracker, nearly 2.1 million people have been infected by coronavirus and nearly 140,000 have died, including 90,000 in Europe. Nearly 60% of the world’s population is living under some kind of mandatory or voluntary confinement.

In the US, which has recorded the most deaths of any country, with 30,985 fatalities out of 639,644 reported infections, Donald Trump was due on Thursday to announce guidelines on reopening parts of the country, insisting that his “aggressive strategy” against the virus was working and that “the data suggests that nationwide we have passed the peak on new cases”.

As the head of the United Nations, António Guterres, said only a “safe and effective vaccine” could return the world to normal, adding that he hoped one might be available by the end of the year, the Bill & Melinda Gates Foundation offered $150m (£120m) for vaccine development.

The foundation’s chief executive, Mark Suzman, said the challenge was huge. “There are 7 billion people on the planet,” he said. “We are going to need to vaccinate nearly every one. There is no manufacturing capacity to do that.”

Concern continues to mount over the advance of the pandemic in Africa, where the African Centres for Disease Control and Prevention said on Thursday that more than 1m tests would begin to be rolled out from next week to address a huge shortfall in assessing the true number of cases on the continent.