The infection rate as measured over the past 14 days rose to 163.4 cases per 100,000 people from 151.8 cases on Saturday as a gradual uptick in contagion from mid-March lows continued to gather pace.
Health emergency chief Fernando Simon confirmed infections were on the rise across the country and that pressure on the health system was beginning to build.
However, he stressed the rate of increase remained far milder than in previous waves and that Spain was faring better than neighbouring countries.
In France, where the government imposed a fresh lockdown over the weekend to rein in spiralling infections, new cases surged by nearly 70,000 on Sunday.
By contrast, Spain reported 10,360 cases since Saturday, bringing the overall tally to 3.3 million. The death toll increased by 85 to 75,783.
"What is clearly decreasing is the number of deaths, which has a lot to do with the immunisation of the elderly and the most vulnerable," he told a news conference.
Spain took delivery of 1.2 million doses of the Pfizer-BioNTech shot on Monday and will receive a similar amount each week throughout April, Health Minister Carolina Darias told a separate news conference.
The objective of inoculating 70% of the 47 million strong population by the end of summer is "within arm's reach," she said.
Data released on Monday showed around 5.7 million people had received at least one shot, while 2.8 million had received a full course of two doses.
"We are on track to achieve collective immunisation," Darias said.
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