* Campaign heats up with less than one month to Oct. 7 vote
* Chavez says he guarantees prosperity for wealthy voters
* Opponent Capriles appeals to poor in new TV spot
By Andrew Cawthorne
CARACAS, Sept 10 (Reuters) - Venezuela's famously anti-capitalist president, Hugo Chavez, has urged rich voters to back him or face "civil war," while his opponent sought to reassure the poor he will not abandon popular socialist welfare policies if he wins next month's election.
Chavez, 58, and Henrique Capriles, 40, face off in an Oct. 7 vote for the presidency of the South American nation of 29 million people, which has the world's largest oil reserves and is a financier of leftist governments around the region.
Though Chavez leads the majority of Venezuela's best-known polls, Capriles' numbers have been creeping up in recent weeks and he is just ahead in a couple of them, leaving each side to believe it has a strong chance of winning the presidency.
Having made a political career of bashing the rich for all Venezuela's ills - and indeed the world's - the socialist Chavez turned to them in a campaign speech late on Sunday, warning wealthy voters they should back him if they wanted stability.
"The rich families have their families, fine houses, good vehicles, probably an apartment at the beach, properties and so on. They like to travel abroad for holidays," he told a rally.
"Does a civil war suit them? Not at all. It only suits the extreme, fascist right embodied by the loser. It's in the interests of the peace-loving rich for Chavez to win, and I invite them to vote for Chavez on October 7. Chavez guarantees peace, stability and economic growth."
Chavez does not use Capriles' name in public, routinely referring to him with the insulting epithet "majunche," which can be loosely translated as "loser," and insisting his supporters have violent plans to end socialism in Venezuela.
The opposition dismisses Chavez's frequent comments about possible civil war as irresponsible scaremongering, pointing out Chavez himself led a failed military coup in 1992.
The president remains immensely popular among Venezuela's poor, in part because of his own humble roots and folksy style, and also due to oil-funded welfare projects like subsidized food stores, and free healthcare and education.
In a campaign projecting his energy and attention to day-to-day problems, state Governor Capriles has been crisscrossing Venezuela, visiting hundreds of towns and villages, especially those where support for Chavez is strongest.
On Sunday night, in a message broadcast on private TV channels, Capriles tackled head-on one of the main fears of traditional Chavez supporters - that he will abandon the social "missions" that are the president's flagship policy.
"My commitment is to create new missions, keep the current ones and improves those which don't work," Capriles said, noting that as Miranda governor he ran a "Zero Hunger Plan" providing food for thousands, as well as improving schools and clinics.
A lawyer by training but a professional politician since his mid-20s, Capriles unexpectedly beat a heavyweight Chavez ally to win the Miranda governorship in 2008 and has won wide respect for his work there since.
Though U.N. data back the government's line that poverty has been reduced under Chavez, the opposition says he should, in fact, have achieved far more in terms of social welfare given the bonanza of oil revenues since he took office in 1999.
"A while ago, we proposed a Missions Law, so that they do not depend on the government of the moment and reach all needy Venezuelans, irrespective of their political color," Capriles said.
Specifically, the subsidized Mercal food chain should be expanded to end long lines and offer greater variety, while slum clinics currently staffed by Cuban doctors should also be opened to local medics, he said in his TV message.
Polls are notoriously controversial and divergent in Venezuela. Among the myriad public opinion companies, respected Datanalisis put Chavez ahead by 12 points in July. Another well-known pollster, Consultores 21, has Capriles just ahead.
Despite predictions by some of a violent election campaign in Venezuela, where society is both deeply polarized and awash with guns, there have only been a few incidents in the last few months of shootings or scuffles.
Underlining the potential for trouble, however, Capriles canceled a weekend visit to a Caracas slum, alleging that armed government gangs were waiting for him there.