Italy, the country with the world's worst outbreak, reported 602 more deaths in the last 24 hours, with the overall number to 6,077.
The number of confirmed cases in Italy rose to 63,928 from 59,138 on Sunday, an increase of 8%, according to the Civil Protection Department.
However, it was the lowest rise in percentage terms since the contagion in the country came to light on 21 February.
Lothar Wieler, head of the country's health institute, said: "We are seeing signs that the exponential growth curve is flattening off slightly.
"But I will only be able to confirm this trend definitively on Wednesday."
Mr Wieler added that he was optimistic, given the strict measures in place in Germany, including those on public gatherings and washing of hands.
In Spain however, cases have continued to surge, with 4,517 more people diagnosed with COVID-19 in the last day - a rise of 15% on the previous day.
The total number of confirmed cases in the country stands at 33,089 - the second highest number in Europe. 2,182 people have now died in Spain, after testing positive for COVID-19.
More people have died after testing positive from coronavirus in Italy than anywhere else in the world - despite the stringent lock down measures in place.
Elsewhere, the number of dead in Iran continues to rise, with 1,812 people losing their life after testing positive, out of 23,049 confirmed cases.
Elsewhere around the world:
Iran is facing widespread criticism for not enacting stricter social distancing and quarantine measures earlier on in its outbreak, like other countries nearby.
The epicentre of the global outbreak in Wuhan in China, has gone a fifth day in a row without any new infections, according to the country's health ministry.
China implemented very strict quarantine measures, which are now being slowly relaxed, that have led to a slow down in the country's infection rate.
Chinese officials have also said the US is trying to "scapegoat" the country and called on it to "stop politicising the epidemic".
Those calls to the US come as President Donald Trump continues to call the virus the "Chinese virus". The US is also seeing a dramatic rise in cases - with 35,241 confirmed cases so far and 473 deaths linked to COVID-19.
Several states have ordered residents to stay indoors with official orders, including New York, California and Illinois.