* Tensions run high after Chavez's death last week
* Maduro demands apology from Capriles over Chavez comments
* Capriles says debate should focus on daily problems
Venezuela's opposition leader challenged acting President Nicolas Maduro on Thursday to "stop lying" and have a debate, adding that he was sorry if he had caused offense during the increasingly bitter run-up to an April 14 election.
The death last week of socialist leader Hugo Chavez set the stage for the vote pitting Maduro, his preferred successor, against Henrique Capriles, a 40-year-old centrist state governor.
Capriles has enraged Maduro by accusing him of repeatedly lying about the late president's two-year battle with cancer, and of then cynically using his death as a campaign tool. But he apologized if he had upset Chavez's family.
"Let's debate, Nicolas, the country wants us to. We've got a month to do it. Let's debate the insecurity and the economy ... . The country wants you to stop lying and debate the problems and their solutions," Capriles told a local radio station.
"If any word of mine was misunderstood, if any word hurt the feelings of the president's relatives, forgive me."
Maduro, a 50-year-old former bus driver and union leader, has said he would consider a debate with Capriles if his opponent retracted his comments and apologized publicly for "the very grave offense" he had given against Chavez's memory.
"He can attack me all he wants, I don't care. I'm ready for it," Maduro said late on Wednesday. "If he apologizes publicly to the family and the people, I would consider having one public debate, or as many debates as the people want."
Capriles lost a presidential vote to Chavez in October, and two recent opinion polls have given Maduro a solid lead over the Miranda state governor.
At stake in the upcoming election is the future of Chavez's leftist "revolution" and the continuation of Venezuelan oil subsidies and other aid crucial to the economies of leftist allies around Latin America, from Cuba to Bolivia.
Venezuela boasts the world's largest oil reserves.
One of Chavez's daughters, Maria Gabriela, published an open letter to the "sick opposition" this week, accusing them of "playing with the pain of a nation and a devastated family."
Government supporters, who have used racial and homophobic slurs against Capriles, dismissed his contrition.
"The princess has spoken," former information minister and Maduro campaign member Andres Izarra said on Twitter. "He wants to debate, but without apologizing. That's to say, he is a scoundrel and he's scared."
In a dramatic twist to the already volatile campaign, Maduro said on Wednesday that there was a plot to kill Capriles by "far right" U.S. elements linked to two senior former members of the George W. Bush administration.
The allegation was similar to the frequent claims of U.S. plots that Chavez made during his 14-year rule. The opposition dismissed those as a ruse to create a sense of "imperialist" threat and distract voters from daily problems.
The two former U.S. officials named by Maduro - Otto Reich and Roger Noriega - called the accusations outrageous and untrue.
On Friday, Chavez's body is due to be carried to a hilltop museum from the military academy where it is lying in state and has been viewed by million of Venezuelans.
The government had planned to embalm his remains and put the body on display in the style of communist leaders Lenin, Stalin and Mao. But Maduro said it might not be possible because embalming may have started too late after death.
Adding to the famous faces who have visited Venezuela to pay their respects to Chavez, Major League baseball star Sammy Sosa arrived in Caracas late on Wednesday.
"Sadly, we lost a humble, spiritual and Christian person," the Dominican-born player told reporters at Maiquetia airport.