By Andrew Cawthorne and Girish Gupta
CARACAS (Reuters) - Venezuelan opposition leader Henrique Capriles demanded justice on Sunday for the shooting of three of his activists, while President Hugo Chavez promised to expand his socialist agenda if he wins next weekend's election.
With a week to go, Venezuela's presidential race looks close and tensions are rising. On Saturday, gunmen killed three pro-Capriles activists in Barinas state - the worst violence of the campaign.
"Yesterday, sadly, violence took three lives, something that should never have happened," Capriles told hundreds of thousands of exuberant supporters at a rally in Caracas that appeared to be the largest of his campaign.
"I want to tell their families, and those angels in heaven, that we are going to defeat violence on the 7th of October."
Capriles' Primero Justicia (Justice First) party said the assailants had fired from a van that witnesses identified as belonging to a state agency, after Chavez supporters had blocked an opposition motorcade.
The government did not admit fault in the shooting, but promised an investigation into what it said was an isolated incident in the South American nation of 29 million people.
Chavez said he regretted the deaths and called for calm, while at the same time saying any confrontation would come from the "bourgeois" opposition.
"It's not with violence that we face off. It's with votes, ideas, peace, so let's not fall into provocations," Chavez said during a rally in western Zulia province.
Venezuela is awash with arms, and voters cite violent crime as their No. 1 concern. There have been gunshots and clashes at previous opposition rallies, but no deaths.
Capriles has hammered Chavez daily for his record on day-to-day problems like crime, blackouts and shoddy infrastructure and drew a frank response from the president.
"Efficiency, that is one of my promises for the next period. We have to correct things," the 58-year-old Chavez said on Sunday in his most direct comment on a theme the opposition hopes could sway former "Chavistas" into their camp.
Chavez has acknowledged Venezuelans' frustration with grassroots problems in his recent campaign speeches, but said things would be far worse under Capriles, who he paints as a heartless capitalist elitist.
Capriles, 40, is a state governor with a centrist view of a Brazilian-style, pro-business government with strong welfare policies. Both men have spent time in prison - Chavez for a failed military coup in 1992 and Capriles for a fracas outside the Cuban Embassy during a short putsch against Chavez in 2002.
With one week to go, polls are mixed, leading both sides to claim they are heading for victory. Venezuelans are fearful of violence if the result is close and disputed.
Of the six best-known pollsters in Venezuela, a majority put Chavez ahead, but they also show Capriles creeping up in recent weeks. Two polls put Capriles just ahead of Chavez.
Despite two bouts of cancer since mid-2011, Chavez has declared himself completely cured and is trying to recapture his old energy to win another six-year term.
He was campaigning in two states on Sunday.
Western investors hope the more business-friendly Capriles will win and end a nationalization drive and other radical policies that have polarized Venezuela and made Chavez one of the world's most controversial leaders.
"I will not aspire to be a Messiah," Capriles told the rally, saying Chavez was more interested in a grandiose self-image than in solving Venezuela's problems.
Chavez has directed a large part of the OPEC member's oil revenues to social welfare projects popular with the nation's poor. He also maintains a unique connection with the masses, thanks to his folksy rhetoric and own humble roots.
On Sunday he promised to "deepen" socialism if he wins.
That would likely mean continued spending on his popular welfare "missions," more investment from politically aligned allies like China and Iran, new confrontations with Venezuela's private sector and continued support for fellow leftists governments in Latin America like Cuba and Nicaragua.
"The first thing we are going to do with our victory is something like put a lockdown on what we have achieved, to prevent any going backwards. That would be terrible," Chavez said in an interview on state TV.
After election wins in the past, Chavez has launched nationalization or constitutional reform drives.
Opposition leaders are angry at Chavez' use of state resources in his campaign, but say the electronic-based voting system should be hard to rig on election day, since they will have their own observers at most voting booths.
Some Capriles supporters, who regard Chavez as a dictator, believe he would refuse to accept defeat.
"Chavez will definitely put up a fight because he does not want to lose power," said Vessla Rodriguez, 62, waving a huge flag with Capriles' slogan "There is a way" at the march.
"Just look at Fidel Castro," she added, in reference to Chavez's friend and mentor who led Cuba for decades.
(Additional reporting by Helen Murphy, Enrique Andres Pretel, Eyanir Chinea, Marianna Parraga and Mario Naranjo; Editing by Stacey Joyce)