Spain announced 331 new virus deaths Monday in a slight increase on its lowest daily figure in month, as officials warned parents not to flout rules after children were allowed outdoors.
The coronavirus has killed 23,521 in Spain, the third-highest death rate in the world, but on Sunday the overnight toll fell to 288.
That was the lowest 24-hour figure in more than five weeks, raising hopes the worst of the outbreak may have passed.
Officials believe the epidemic peaked on April 2 when the daily toll hit 950.
Spain's nearly 47 million people have spent more than six weeks under one of the strictest lockdowns in the world, with only adults authorised to leave home to buy food, medicine or walk the dog.
A first move to ease the restrictions went into force on Sunday when kids under 14 were allowed out for the first time to go for a walk, a run or a bike ride accompanied by one parent.
Under the new rules, children are allowed out for up to an hour a day within a one-kilometre (0.6 miles) radius of their homes, but are barred from gathering in groups.
But officials warned against anyone flouting the rules, saying police broke up several gatherings of "children playing together" and "groups of parents chatting".
"There must be no more abuses," warned Health Minister Salvador Illa.
- 'Costly mistakes' -
Officials said fines would be issued to anyone who failed to abide by the regulations.
"We will not allow any mistakes" because it could "cost us a lot", Interior Minister Fernando Grande-Marlaska said.
Spain has so far counted more than 210,000 cases of COVID-19, the second-highest figure in the world, although the health ministry only logs cases confirmed by diagnostic tests.
The number of people who have recovered from the virus now stands at well over 100,000.
Until late last week, the government was also including the numbers of those shown to have developed antibodies against the virus.
On Monday, the government began a sero-prevalence study involving 60,000 people to collect information on the real number exposed to the virus through analysing blood test data.
Raquel Yotti, head of the Carlos III Health Institute, said the study would allow experts to get a real picture of "the number of people who have been in contact with the virus" and developed antibodies.
"It's important to know the spread of the virus at a national, regional and local level," Yotti said.
Spain's lockdown is set to remain in place until at least May 9, and the government may take further steps to ease restrictions in the second half of the month.
Madrid has been the worst-hit area, accounting for 34 percent of all deaths.
But the situation has improved to the extent that this week officials are expected to close a huge field hospital set up on the eastern outskirts of the city.