Confirmed cases of Covid-19, the disease caused by the virus, rose to 64,059, a 14% increase compared with 18% a day earlier and 20% on Wednesday.
In 24 hours, 769 people died, a daily record, taking the total to 4,858.
Nursing home residents are particularly affected. Spain is Europe’s second-worst-hit country after Italy.
The Spanish government has extended the state of emergency until at least 12 April. People’s movement are severely restricted and most shops and businesses closed.
The latest figures raised hopes that the measures were beginning to take effect. Health emergency chief Fernando Simón said they showed a “clear stabilisation” and that it seemed they were “approaching the long-awaited peak”.
Across the country, the army has been deployed to deep-clean hospitals and other facilities – including some 900 nursing homes where at least 1,517 deaths have been recorded.
Hospitals have been under intense pressure, and the number of confirmed cases included 9,444 health workers. For days, doctors, nurses and other frontline personnel have complained of inadequate protective equipment.
Meanwhile, the health ministry said some 9,000 rapid diagnostic tests imported from China had proved defective. Their use has been suspended, it said.