High temperatures across Spain resulted in three "record days of heat" that began on Friday, with the mercury peaking on Sunday at 38.2°C in the southern town of Montoro near Cordoba, the bureau said.
The previous October record was set in 2014, when the mercury hit 37.5°C in the southern town of Marbella.
"On October 1, it reached an all-time high for this time of year in practically the entire Iberian Peninsula," Aemet said on X, formerly Twitter.
It said that nearly 40 per cent of its weather stations had registered a temperature of 32°C or higher.
The situation was similar on Monday, with the southern city of Seville reaching 38.1°C, its figures showed.
"But the most extraordinary thing is that there are still quite a few unseasonably warm days left. We could have up to 10 more days of record heat," Aemet said.
Although it has become accustomed to soaring summer temperatures, notably in the south, Spain has experienced a sharp rise in longer and hotter heatwaves, experts say.
The country, which had its hottest year on record in 2022, has been in the grip of successive heatwaves this year, which began unusually early in April, exacerbating a continuing drought.
Experts say the recurring heatwaves, which have been getting longer and more intense, are a consequence of climate change.
The Iberian Peninsula is bearing the brunt of climate change in Europe, with droughts and wildfires increasingly common.