Italy and France both reported an increase in their daily death toll due to coronavirus on Monday, after a decline in deaths in recent days.
France reported 605 new deaths in hospital from coronavirus in one day on Monday, compared to Sunday's 357 and Saturday's 441.
The country also reported 228 new deaths in nursing homes or EHPAD.
This total of 833 new deaths in one day is the highest in France since the start of the pandemic.
In total, 8911 people have died of the coronavirus in France, the French Health minister Olivier Véran said, and 23,620 coronavirus cases have been confirmed.
Italy's deaths due to coronavirus also increased on Monday.
There were 636 new deaths on Monday compared to 525 on Sunday, the lowest recorded death toll in more than two weeks.
In total, 16,523 people have died in Italy from COVID-19 and there are 93,187 confirmed coronavirus cases.
Italy has more recorded deaths than any other country in the world.
Monday's death toll contradicted officials, who on Sunday had said that the numbers showed that the country likely was past the peak of the epidemic.
Italy's health minister warned on Sunday that the situation is still "dramatic" and that there would be "difficult months ahead".
Officials in the country have said that the movement restrictions in place have saved thousands of lives.
In the UK, the death toll due to coronavirus passed 5,000 on Monday as the country reported 439 new deaths.
There have now been 5,373 deaths and 51,608 confirmed cases in the UK, including British PM Boris Johnson, who has been in hospital since Sunday.
Latest figures from Spanish health authorities continue to show a decline in the number of new cases and deaths from coronavirus.
The number of new confirmed cases represents a fall for the fourth day in a row, suggesting strict social distancing measures have begun to show their effects.
More people are continuing to be infected and die from the virus, but at a slower rate compared to last week.
The number of new confirmed cases fell to 4,273, Spain's health authority reported on Monday, compared to more than 6,000 new cases on Sunday and over 7,000 on Saturday.
The number of deaths from coronavirus in 24 hours also fell for the third consecutive day to 637, officials said, down from 674 on Sunday and 809 on Saturday. It's the lowest daily increase since March 24, but takes the total number of deaths to over 13,000.
Meanwhile, a further 2,357 people were reported to have recovered from the virus on Monday, bringing the total to over 40,000.
Germany's Chancellor Angela Merkel said on Monday that the coronavirus pandemic was "the biggest challenge" to the EU since its foundation. The response to this crisis, she said, must be "more Europe, a stronger Europe, a Europe that works well".
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Relaxing lockdown measures not yet an option in Spain
The decline in the coronavirus death and infection rate in Spain is encouraging news for health authorities, often overwhelmed by the pandemic in the worst affected country in Europe after Italy.
In a press briefing on Sunday, Maria Jose Sierra, from the Centre for Health Alerts and Emergencies, said "one in three" patients with coronavirus had now recovered, before laying the next steps of the "de-escalation" of the crisis.
She said the government's goal would eventually move into a stage of testing everyone with symptoms of the virus, and confirmed that "serious" studying of the effectiveness of face masks was underway.
Spanish Prime Minister Pedro Sanchez told citizens on Saturday that the country was finally "in a position to bend the curve".
But in a press conference, he announced an extension to the three-week lockdown - to April 25 - warning that Spain was not yet out of the woods.
He said: "If the climb has been hard, let's not fool ourselves, the descent will not be smoother. We are facing the great crisis of our lives."
On Friday, Spain surpassed Italy to become the second worst virus-hit nation in the world - behind that of the United States.
Therefore, any consideration of relaxing stringent lockdown measures during this time "would have a worse result than returning to the starting point," Sanchez said at the conference.
He added: "The victory that puts an end to it will only come with a vaccine that unfortunately will take a few months."
Spain's total number of COVID-19 infections rose to above 135,000 on Monday, while more than 13,000 people have lost their lives.
Surge in UK cases over the weekend
Boris Johnson spent Sunday night in hospital to undergo tests for "persistent" coronavirus symptoms after being diagnosed with the illness ten days ago. He said on Twitter on Monday that he was "in good spirits" and is still officially in charge of government.
Meanwhile, Queen Elizabeth II compared the unfolding coronavirus pandemic to World War II in an address to the British public.
These developments came as there was a surge in cases of coronavirus in the United Kingdom with more than 5,900 new cases and 600 deaths in 24 hours. The increase in cases could be due to an increase in testing capacity.
"The only effective way of bending the curve down is to reduce that social contact," said health secretary Matt Hancock, who recently recovered from COVID-19. He said the government had been "crystal clear" about the rules and that the evidence shows a "high proportion" of the public are following them.
He said that following the rules was "mission critical" and told the "minority" of people breaking rules that they were risking their lives and the lives of others.
Hancock said that even though people who have recovered are likely immune, scientists do not yet know enough to be able to change social distancing rules.
Dr Jenny Harries, the deputy chief medical officer for England said that the government was testing in care homes and prisons, where there have been outbreaks.
Meanwhile, Scotland's chief medical officer Dr Catherine Calderwood resigned after reportedly visiting her second home in violation of social distancing measures in place to prevent the spread of Covid-19.
After apologising, she said the "justifiable" focus on her behaviour "risks becoming a distraction from the hugely important job that government and the medical profession has to do in getting the country through this coronavirus pandemic."