Voters had been angered by the insistence of the ruling Popular Party that Eta was to blame for the bombing that killed 191 people, despite evidence that pointed to an al-Qaeda inspired attack.
An estimated 25 million are eligible to vote to elect the 350 members of the Cortes, the lower house of parliament, as well as 208 of the 264 members of the Senate, or upper house.
Polling stations opened at 9am and will close at 8pm (0800GMT to 1900GMT). Official results are expected on Sunday night. Eta 'interfering'
Police believe that the banned Eta movement, which has been blamed for the deaths of more than 800 people in bombings and shootings in a nearly 40-year campaign for an independent homeland, killed Carrasco.
|"I call on those who want to show solidarity with my father and with our pain to vote en masse Sunday"|
Zapatero has accused Eta of interfering with the electoral process, although have been no claims of responsibility so far.
Carrasco's eldest daughter, Sandra, called for Spaniards to vote in order to defy Eta.
"I call on those who want to show solidarity with my father and with our pain to vote en masse Sunday and tell the murderers that we are not going to take a single step backward," she said.
The PP has criticised Zapatero's failed attempts to negotiate peace with Eta during his first term, but during campaigning it focused on the slowing economy and the rapid rise in immigration.Popular measures
Zapatero campaigned as the face of a modern, progressive Spain after brining in popular liberal measures such as same-sex marriage, fast-track divorce and a gender-equality law.
Opinion polls suggest that the socialists will be re-elected but they would once again fall short of an absolute majority.
Following the 2004 elections, Zapatero was 12 seats short of an absolute majority in the lower house of parliament.
For the past four years he has governed with the support of smaller regional and left-wing parties.