The explosions, minutes apart, caused substantial damage in the resorts which are popular with British tourists as well as other Europeans.
Injuries could have been worse but those behind the attacks made calls to the media warning them in advance about the bombs.
Authorities now fear this could herald the start of a summer campaign by Basque separatists to disrupt Spain's lucrative tourist industry.
The first explosion injured eight people, two seriously, at the Hotel Bahia in Alicante. The second blast at the Hotel Nadal in nearby Benidorm injured four policeman who were cordoning off the building.
Police said one Alicante victim was a 22-year-old German student, while a Foreign Office spokesman in London said a British woman had been treated for minor injuries.
The hotels were evacuated minutes before the devices exploded at around midday (1000 GMT), following an anonymous call to the Basque newspaper Gara by someone claiming to represent the armed Basque separatist group ETA. The caller said the blasts would occur around 12:30pm, at least 15 minutes later than they actually took place.
Basque separatists have killed more than 800 people in a violent campaign, stretching over three decades in an attempt to create an independent homeland in northern Spain.
Juan Cotino, the Spanish government delegate in the autonomous region of Valencia, confirmed that eight people were known to have been hurt but said the toll could rise, telling Spanish television that both hotels had been evacuated as quickly as possible.
Aznar, welcoming visiting Irish Prime Minister, Bertie Ahern, reacted combatively, vowing to hunt down the bombers.
"I am absolutely convinced we will soon see those behind what happened today in prison," said Aznar, who promised "ever tougher sentences" for those responsible for the blasts.