Spain saw its death toll fall for the fourth consecutive day as 637 new fatalities were confirmed today, marking the lowest daily total since March 24.
The Spanish government is now contemplating a gradual easing of the lockdown, which has been in place since mid-March.
Italy, which is the only country to suffer more deaths than Spain, is also showing signs of recovery as the daily number of deaths appear to be reducing.
"The pandemic's growth rate is slowing down in almost every region," Maria Jose Sierra, deputy head of Spain's health emergency committee, said at a virtual news conference.
The country's latest death toll stands at 13,055, with 135,032 infections - up from 130,759.
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This is a 5.1 per cent rise in new fatalities and a 3.3 per cent jump in fresh cases, the lowest rate of increase since the country entered lockdown, Mail Online reports.
It comes after Spain recorded 950 coronavirus deaths on April 2 - the highest daily figure so far.
Officials said for restrictions to be lifted, testing had to be widened beyond those suspected of having the COVID-19 disease and health workers, so as to find carriers who may have no symptoms or only very mild symptoms.
"We are preparing ourselves for de-escalation for which it is important to know who is contaminated to be able to gradually lift Spanish citizens' lockdown," Foreign Minister Arancha Gonzalez told TV station Antena 3.

Spanish companies are manufacturing 240,000 test kits per week and are boosting capacity, the foreign minister said, while equipment is also being bought from abroad.
Spain has been in lockdown since March 14, with streets and famous tourist sites eerily silent. Prime Minister Pedro Sanchez said at the weekend that would remain in place until April 26.
Though starting to hope for an end to their torment, Spaniards were also venting frustration on social media at the lengthy stay-at-home.
"I'd love to be in a bar, listening to good music and accompanied by many litres of beer - but no, I'm lying in bed and already sick of this confinement," tweeted one Spaniard.
"I only hope at some point we return to normality."
One mother, Sandra Eva, said her four-year-old girl was upset at missing Easter traditions.
"She asks me why we can't go out to watch the Easter processions. That it's not fair. That she wants to see them. And that she's tired of the coronavirus," she tweeted.