A risk report by the European Centre for Disease Control and Prevention (ECDC) said its mortality monitoring system showed that deaths from all causes, including COVID-19, are above expected rates in Belgium, France, Italy, Malta, Spain, Switzerland and Britain, mainly in over 65s.
Despite early evidence from Italy and Austria that the numbers of cases and deaths are declining, "there is currently no indication that the peak of the epidemic has been reached", the assessment said.
Andrea Ammon, the ECDC's director, said that based on the available evidence in the region and in the current situation, "continuous spread of the virus can be expected".
Led by Italy, much of Europe has gone into lockdown in recent weeks, with schools and businesses closed and citizens ask to stay at home as countries seek to limit the spread of COVID-19, the respiratory disease caused by the new coronavirus.
"It is still too early to suddenly lift all community and physical distancing measures...even though these stringent measures may be quite disruptive to society on an economic and social level," she said in a statement with the report.
The ECDC's assessment follows a warning earlier on Wednesday from the World Health Organization's European director Hans Kluge, who described the region's outbreak as "very concerning".
"We still have a long way to go in the marathon," Kluge said, and urged governments to give "very careful consideration" before relaxing social distancing and lockdown measures put in place to try and control the disease's spread.
Ammon said coordination between European Union member states would be essential in "the de-escalation phase", when the peaks have passed and societies are beginning to open up again.
This would aim to "minimise the risk of infection ‘spilllover’ between countries if they de-escalate at different rates and in different ways," she said.