The vote is an important test of Chavez's support a year after Venezuelans rejected his attempt to abolish term limits, and critics say he is resorting to browbeating and smears for fear his candidates will lose.
"He has unleashed a wave of intimidation," Manuel Rosales, the opposition governor of Zulia state, told The Associated Press.
Rosales, who has a good chance of defeating the Chavez candidate for mayor of Maracaibo, Venezuela's second-largest city, said the socialist leader "wants to wipe out and criminalise Venezuela's opposition, or those who don't think like he does, to attempt a constitutional reform allowing him to remain in power."
During a fiery speech to supporters on Tuesday, Chavez threatened to shut down any television stations that broadcast early election results, and said he has ordered secret police "to keep a close eye on" Rosales.
"That criminal must go to prison," Chavez thundered, noting that Rosales has been repeatedly accused of graft.
"There's evidence. They are not unfounded attacks."
Chavez also has threatened to cut off national funds and send tanks into the streets of states that end up in the hands of opponents, and he ordered soldiers to temporarily seize an airport in a dispute with the opposition governor of Sucre state. Chavez supporters cheered the seizure - and then looted the offices of an opposition mayor the next day.
"This is an armed revolution and the people are willing to defend the revolutionary process," the socialist leader warned last week as he predicted a violent opposition response to his allies' victories.
Chavez allies deny any government-organised effort to intimidate opponents.
But rival politicians, media personalities and other critics blame the president for the bullying by pro-Chavez thugs, campaign-season criminal investigations, and bureaucratic nightmares such as hours-long interrogations by immigration officers at airports.
Authorities say these are routine immigration procedures, but Venezuelan sociology professor Heinz Sontag, who belongs to the opposition 2-D Movement, blames Chavez for the annulment of his valid passport when he returned from a trip last month.
"I think he perceives growing discontent, and he is reacting with rage," Sontag said.
Chavez has been particularly critical of Rosales, his leading opponent in the 2006 presidential race. He traveled to Zulia last month and called for Rosales to be imprisoned, accusing the governor of corruption and even of plotting his assassination. Within days, Venezuela's top anti-corruption official, attorney general and a committee of pro-Chavez lawmakers opened probes.
"Any citizen suspected of corruption or plotting to kill the nation's leader, regardless of their political leanings, should be investigated," lawmaker Mario Isea said.
Isea presented recordings of Rosales' phone calls as evidence he pocketed revenue from a state lottery and could be funding a purported plot aimed at killing Chavez. The purported conversations are repeatedly broadcast in ads mocking Rosales on state television. Isea says the recordings were received from anonymous sources, but Rosales believes they are carefully edited "montages" of his conversations, recorded and pieced together by Venezuela's Disip secret police and Cuba's G-2 spy agency.
"They change words, construct phrases, sentences, and later they put them on the air," Rosales told the AP.
Chavez, a former lieutenant colonel who has been in office since 1999, still has broad support despite the loss of a constitutional referendum that would have expanded his power and scrapped term limits that bar him from running in 2012.
Now he's suggesting that Chavista victories on Sunday could pave the way for another referendum to extend his rule.
"Be aware, Chavez's destiny is even at play," he said at rally last week.
Chavez's allies swept the last state elections in 2004, winning all but two of 23 governorships and a majority of local offices. This time candidates are competing for 22 governorships and 328 mayoral posts, and the opposition is hoping to regain lost ground.
A poll by the Caracas-based polling firm Datanalisis last month found gubernatorial races in 12 states were close, while pro-Chavez candidates led strongly in six states and the opposition in four, said pollster Luis Vicente Leon. The survey of 1,300 adults, paid for by Venezuelan businesses, had an error margin of 2.7 percentage points.
The same poll found Chavez's popularity rose to 56.9% after dipping to 46% in January. The government has cited other polls showing higher presidential approval and more races likely to be won by allies.
But voters are increasingly upset over problems including recurring power outages, a coffee shortage, inflation of more than 35% in Caracas and widespread crime. The number of murders in Venezuela has soared from less than 6,000 during Chavez's first year in office to more than 13,000 last year, according to official figures.
Passions have grown during the campaign - and it seems that the more public the criticism, the tougher the response.
One angry group recently tossed tear gas canisters into the El Nuevo Pais newspaper office with leaflets targeting opposition editor Rafael Poleo as "a military objective."
"It was a veiled death threat, but I won't allow myself to be intimidated," Poleo said.
"Chavez is the one who's scared, and it shows."
