MADRID, Spain (CNN) -- Moments after his challenger conceded, Prime Minister Jose Luis Rodriguez Zapatero thanked a crowd of cheering supporters for Sunday's win by his Socialists in Spain's parliamentary elections.

"The Spanish have spoken with clarity, and they have decided to open a new chapter," Zapatero said."I will govern with a firm hand and with the hand extended."

With 89 percent of the vote tallied, Zapatero's Socialists had 44 percent of the vote, followed by Mariano Rajoy's conservative Partido Popular with 40 percent. Sunday's turnout was put at 75.4 percent late in the day.

Zapatero has ruled with a plurality since 2004, when he and Rajoy first faced each other in a general election, and the prime minister faced concerns about a faltering economy going into Sunday's vote.

"The economic problems have hurt everyone. The prices have risen sharply for all of the daily needs," said Manuel Lustres, a security guard who voted for the Partido Popular.

The vote was also shadowed by the death on Friday of a former Socialist town councilman, Isaias Carrasco, who was killed in an attack in northern Spain blamed on Basque separatist group ETA.

"Isaias should be here today, living this moment and alive with his family," Zapatero said Sunday night.

The 2004 election, held in the wake of the Madrid train bombings that killed 191 people, gave Zapatero's Socialists an upset victory. Zapatero's first decision upon taking office in 2004 was to pull Spain's troops out of Iraq.

Zapatero has put Spain in the vanguard of European social policy, legalizing gay marriage and making divorces easier to obtain. Roman Catholics staged a mass demonstration in Madrid last December to blast the government policies.