MILAN—Europe is catching up with the U.S. in Covid-19 vaccinations and could sprint ahead as the continent overcomes a stumbling start while parts of America struggle with vaccine hesitancy.

Some European Union countries, including Italy, Denmark and Belgium, have already passed the U.S. by the number of people who have received at least one vaccine dose, according to figures compiled by Our World in Data, an Oxford University project tracking the global vaccine rollout. The U.S. is still ahead of the bloc as a whole, with about 54% of people partially vaccinated, compared with 49% in the EU.

A quick vaccine rollout is key for keeping infection rates down and deaths to a minimum, and opens the prospects to a faster economic rebound. The speed with which people are vaccinated has become even more critical in recent weeks as the highly transmissible Delta variant spreads rapidly across Europe, threatening to upend progress made in lowering the infection rate and the economy’s rebound.

Early this year, Europe’s vaccine rollout quickly fell about six weeks behind the U.S.’s. Europe took longer to approve the first vaccines and then suffered from delivery delays and a lack of infrastructure to administer shots on a mass scale. The kinks eventually got worked out and now the continent is vaccinating people at a much faster rate.

People wait after receiving the Pfizer-BioNTech Covid-19 vaccine in Nantes, France.

People wait after receiving the Pfizer-BioNTech Covid-19 vaccine in Nantes, France.

Photo: stephane mahe/Reuters

In the U.S., the number of daily doses peaked in April at 3.4 million and has been declining rapidly since, according to the Centers for Disease Control and Prevention. Last week, an average of about 600,000 daily doses were administered, down from more than one million two weeks earlier. The White House recently said the U.S. wouldn’t reach President Biden’s goal to vaccinate 70% of the adult population with at least one dose by July 4.

In a sign of the slowdown, U.S. states have closed most of their mass vaccination sites. The relatively low number of those waiting for a second dose in the U.S.—8% compared with 26% in Italy—could also indicate its vaccination campaign is stalling, according to some public-health experts.

The number of doses administered in the EU has risen steadily since the beginning of the year and has averaged about 3.7 million daily over the past four weeks, according to the European Center for Disease Prevention and Control. There was a small decline last week that could be either a blip or the start of a downward trend.

SHARE YOUR THOUGHTS

What will be the ramifications, if any, if more Europeans are vaccinated than Americans? Join the conversation below.

Europe will probably pass the U.S. in the percentage of the population with at least one dose within the next three weeks, said Enrico Bucci, a systems biologist at Temple University who studies epidemics. Soon after, as the percentage of the population that is vaccinated rises, it will become evident whether Europe will face the vaccine hesitancy the U.S. has experienced.

“In the next two to three weeks there might be two different forces pulling Europe in different directions,” said Prof. Bucci. “The Delta variant could push vaccinations up if it creates fear. At the same time, the attrition rate could increase, pushing the vaccination rate down.”

The U.S. still has a considerable lead in the number of people fully vaccinated—46% compared with 31% in the EU. That is a particularly important metric at the moment because the Delta variant has proven to be highly transmissible among people who have had only one dose.

As more U.S. adults get their Covid-19 vaccines, a variety of side effects are emerging. WSJ’s Daniela Hernandez speaks with an infectious disease specialist on what is common, what isn’t and when to seek medical attention. Photo: Associated Press The Wall Street Journal Interactive Edition

The rise of the Delta variant and questions over the staying power of Europe’s current vaccination rate comes at a time when the continent is tentatively returning to a pre-pandemic way of life. Restrictions have been relaxed in several countries in recent weeks. France and Italy recently lifted curfews and rescinded the requirement to wear masks outside.

But the U.K., where the Delta variant is more advanced, recently delayed the removal of its remaining Covid-19 containment measures, such as capacity limits in pubs.

Most European countries, including France, Germany and Italy, should reach about 65-70% fully vaccinated during the summer, but every percentage point above that will take considerable effort, said Roberto Battiston, a professor of experimental physics at the University of Trento in Italy who has tracked data on the pandemic and vaccine rollout.

He cautions against putting too much emphasis on a single number for a country because the situation can vary widely.

“In the U.S., in some states where density is more than 100 times lower than in other states, having vaccinated 30% or 40% might be enough,” said Prof. Battiston. “But then in New York you should aim for a very high percentage because there are so many interactions between people.”

Write to Eric Sylvers at eric.sylvers@wsj.com