France, Italy and Spain have registered the lowest daily death tolls for weeks as they prepare to ease restrictions.
France reported 135 deaths; Spain's 164 were the lowest since mid-March; and Italy's 174 was a two-month low.
Meanwhile French doctor has claimed new tests on samples from patients show the virus was present in the country last year – weeks before the first officially recorded case.
In Russia the virus appears to be advancing, with 10,000 new infections.
But Russia's mortality rate remains low relative to other countries. On Sunday it recorded 58 deaths, taking its total to 1,280.
The UK recorded 315 new deaths and has the third-highest number of deaths behind the US and Italy. However British officials say the outbreak has peaked and the number of new hospital admissions is declining.
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Globally the pandemic has seen nearly 3.5 million people infected and nearly 250,000 people have died.
Was the virus in France last year?
The number of new recorded deaths is the lowest since late March, when only deaths in hospitals were being recorded. The new figures include deaths in care homes and have been declining for several days.
Meanwhile an intensive care chief in the Paris region has told local media that the virus was present in France on 27 December – a month before the first cases were confirmed.
Yves Cohen told BFMTV that his team had revisited negative tests for flu and other coronaviruses on 24 patients who had been in hospital with respiratory symptoms in December and January.
"Of the 24 patients, we had one positive result for Covid-19 on 27 December when he was in hospital with us," he said, adding that the test had been repeated several times to confirm the result.
Dr Cohen said he had reported the case to the regional health authorities and called for other negative tests from the same period to be retested.
France is planning to lift its lockdown on 11 May, when children will return to school in phases, some businesses will reopen and people will be able to travel within 100 kilometres (60 miles) of their homes without the need for a document giving a reason for their movement.
However on Sunday Health Minister Olivier Veran said this would depend on further falls in the number of new infections, particularly in the worst-affected areas like the Paris region and northeast France.
France also clarified that a rule requiring anyone entering the country to go into isolation for two weeks did not apply to people arriving from EU countries, the Schengen area or the UK.
What's happening in Spain?
Spain's death toll of 164 was the lowest for a month-and-a-half and was more than a hundred down on Saturday's figure.
On Saturday adults were able to exercise outdoors on Saturday for the first time in seven weeks. The lockdown was eased for children under 14 a week ago.
Prime Minister Pedro Sanchez said Spain was reaping the rewards of the sacrifices made during the lockdown, one of Europe's strictest.
On Monday masks will become compulsory on public transport and some small businesses such as hairdressers wiRead More – Source