More than 300 deaths were recorded from Friday to Saturday, more than the previous high of 235 which had been recorded from Thursday to Friday.
Spain also saw a significant increase in confirmed infections in the past 24 hours, with more than 5,000 new confirmed cases of coronavirus.
This brings the total of confirmed cases to 24,926 as at Saturday morning.
The most significantly affected part of Spain is the Madrid area, where almost 9,000 cases have been recorded along with 804 deaths.
Spain now has the third most confirmed infections after China and Italy, while the death toll is fast approaching that of heavily hit Iran (1,433 people).
During the week, Italy’s death toll of 4,032 overtook that of China (3,200) for the first time.