EU authorities are hoping the EMA’s statement could put a problem-plagued vaccination campaign back on track, though it remains to be seen whether the new analysis will overcome mistrust of the AstraZeneca shot among many Europeans.

Many European countries, including Germany, France and Italy, suspended the vaccine’s use over the past week following reports that people who had received it developed rare blood clots, and some had died, further slowing Europe’s already sluggish vaccination rollout.

Those reports compounded the delays and uncertainties surrounding a drive that has left the EU far behind the U.S. and the U.K. in vaccinating its citizens.

AstraZeneca said after the EMA’s announcement and a similar judgment from British health authorities that the opinions affirmed the vaccine’s benefits. “We trust that, after the regulators’ careful decisions, vaccinations can once again resume across Europe,” said the company’s chief medical officer, Ann Taylor.

In a sign of European leaders’ impatience to do that, Italian Prime Minister Mario Draghi said after the EMA announcement that the country would resume giving AstraZeneca vaccinations on Friday. France, Spain and Portugal also said inoculations would resume.

Europe urgently needs vaccine doses because case numbers are rising amid the spread of new virus strains. France on Thursday announce a new lockdown on the Paris region.

Europeans’ reactions to the EMA announcement were mixed. Rita Szigeti, a retired Parisian who earlier this month received an initial dose of the AstraZeneca vaccine and wants her second dose, voiced pleasure with the announcement. But Corinne Graillot, an assistant engineer at a medical school in Paris who hasn’t been vaccinated, said she preferred to wait for a different option.

“They’ve made such a mess of it that people don’t know what to think anymore,” she said. “They’ve flip-flopped so many times.”

The EMA’s safety committee found the vaccine to be “safe and effective in preventing Covid-19, and its benefits outweigh its risk,” said committee chair Sabine Straus. Dr. Straus said that the vaccine “likely reduces the risk of thrombotic incidents overall” since blood clots are associated with Covid-19.

Health officials have noted that blood clots are widespread for a variety of reasons. Clots have also been noted among people receiving other Covid-19 vaccines and can be caused by medications as common as birth-control pills.

EMA Executive Director Emer Cooke said the experts found a limited number of blood clots that require further study, and the agency “still cannot rule out definitively a link.”

Dr. Straus said a predominance of the blood clots found were among women, particularly younger women. She said it remained “premature to conclude” whether this is linked to greater risk among the groups or the makeup of the populations receiving the vaccine.

Attention to potential side effects of the vaccine is growing. Lucía Ejarque, a teacher from Madrid, had high fever and strong headaches for two days after getting the AstraZeneca vaccine on Sunday. Then the arm where she got the shot started hurting and grew inflamed.

“I got very worried,” she said. She saw her doctor on Thursday, who said the symptoms were among those expected and would likely pass, but that if her arm reddened more she should go to the hospital as a caution, including about thrombosis.

Ms. Ejarque said she still trusts the vaccine. “I just hope the pain disappears quickly,” she said.

The EMA on Thursday recommended “raising awareness” by including a warning with the vaccination and informing the public. Such a campaign could help people who receive the AstraZeneca vaccine to know what to look for after getting the shot.

Ms. Cooke on Tuesday had expressed concern that doubts being cast on it could hurt public trust in vaccines. Asked in a news conference Thursday if she personally would get the AstraZeneca shot, she said, “If it was me, I would be vaccinated tomorrow, but I would want to know that if something happened to me,” what to do.

Ms. Cooke, noting that many EU countries had suspended use of the AstraZeneca vaccine pending the EMA’s review, said its conclusions should give them “the information they need to take an informed decision regarding the use of the AstraZeneca vaccine in their vaccination campaigns.”

So far, roughly seven million people in the EU, and 11 million in the U.K., have received the vaccine, Ms. Cooke said. It is the world’s most widely used Covid-19 vaccine.

Analysis of the vaccine took on extra urgency this week after the Paul Ehrlich Institute, Germany’s medicines regulator, Monday recommended suspending the vaccine’s rollout pending further investigation.

Institute President Klaus Cichutek defended the recommendation, saying his experts identified seven cases in Germany of cerebral vein thrombosis, a severe brain condition, and three of the people died. Germany’s healthcare ministry said that, based on the number of vaccinations given, it would have expected as many as 1.4 cases of cerebral vein thrombosis, and the seven cases merited a pause.

The EMA collected reports from across Europe, giving it a much larger data set to analyze.

Some EU countries, including Greece and Belgium, have continued using the vaccine, as have Australia, Canada and India.

The U.K., where AstraZeneca developed the vaccine with scientists from University of Oxford, is relying heavily on the vaccine for its relatively fast vaccination campaign. British politicians have criticized their EU counterparts for suspending the vaccine’s use against expert advice.

Many medical experts in Europe and beyond criticized politicians’ decisions to halt vaccinations, saying the known risks posed by the coronavirus are greater than possible ones from AstraZeneca shots. German officials said their suspension was merited because they are urging citizens to take the vaccine, unlike other medications such as contraceptives, which are a personal choice.

European officials who paused vaccinations framed their decisions as precautionary. But based on available data and Covid-19 risks, “the cautionary approach would be to carry on vaccinating,” said Prof. David Spiegelhalter, an expert on statistics and risk at the University of Cambridge. “Casting doubt—lasting doubt—on the safety of the vaccines is not a precautionary position.”

French Prime Minister Jean Castex on Thursday announced the partial lockdown for Paris and other parts of the country where new variants of the virus are spreading rapidly and intensive-care wards are nearly full.

The decision came as France decided to resume vaccinations with the AstraZeneca vaccine on Friday after the EMA review. Mr. Castex said he would receive the vaccine Friday to reinforce public confidence in its safety and effectiveness.

The new measures will last four weeks and come into effect Friday at midnight, Mr. Castex said. The public will be required to stay within 10 kilometers, or 6.2 miles, of their homes. Mr. Castex urged businesses to have their employees work remotely as much as possible, though businesses and employees will be allowed one day of work in the office.

The lockdown is far less strict than the one France instituted a year ago at the start of the pandemic. Schools will remain open. Outside activities won’t be time-limited. And the government eased a curfew that was already in place from 6 p.m. to 7 p.m.

—Giovanni Legorano, Nick Kostov and Jenny Strasburg contributed to this article.