* Students march on election authority in Caracas
* Stones thrown in clash with government supporters (Adds Maduro comments)
By Deisy Buitrago and Efrain Otero
CARACAS, March 21 (Reuters) - Police fired tear gas in downtown Caracas on Thursday as anti-government student protesters clashed with supporters of late President Hugo Chavez in an increasingly volatile atmosphere ahead of next month's election.
Several hundred students were marching to the election board's headquarters to demand a clean vote when they were blocked by government supporters who hurled stones, bottles and eggs at them, a Reuters witness said.
Some of the students threw stones back, other witnesses said.
"We were holding a peaceful march. ... All we want is democracy," said law student Eduardo Vargas, 19, whose eye was injured in the incident. "We're all Venezuelans. We just want a fair vote."
Police fired tear gas towards the 150 or so government supporters and formed a cordon between the two sides.
It was the first outbreak of violence since an election was called on April 14 for the South American OPEC nation following Chavez's death from cancer two weeks ago.
Both candidates, acting President Nicolas Maduro and opposition leader Henrique Capriles, have been trading personal accusations as they rally supporters for the vote.
One onlooker, Gustavo Malave, a 78-year-old who works for one of the socialist "community councils" set up during Chavez's 14-year rule, blamed the students for starting the trouble.
"The clash began because the opposition started throwing stones," he said. "I support Chavez and Maduro. Chavez set this course, and it's going to continue for 40 or 50 years."
Before the clash, the students had been marching to the election headquarters singing the national anthem and carrying signs including "Free and fair elections" and "Nicolas is a liar."
"The students are saying to the world and to the country that we are in the street. We want transparent and free elections," said one student leader, Victor Fernandez.
Maduro at an evening campaign rally called the students "a small group of recalcitrant right-wing people."
"None of us can ... be provoked by those tiny groups that make a living off hatred," he said.
He said the group had links to two U.S. diplomats expelled on the day of Chavez's death on charges they were attempting to conspire with the Venezuelan military.
"I want you to know that those two men directly gave orders and instructions and money to this same group," he said.
That charge follows a flurry of recent accusations against U.S. authorities including a charge that the State Department is seeking to kill Capriles to spark a coup.
Washington denies the accusation.
With sympathy over Chavez's death galvanizing government supporters, Maduro, 50, a longtime socialist stalwart, is favorite to win next month's vote.
Two polls published this week put the former bus driver ahead of Capriles by more than 14 percentage points.
Capriles, a 40-year-old state governor, accuses Maduro of being a nonentity who is exploiting the emotion around Chavez's death. He wants voters to focus on daily problems confronting Venezuelans ranging from potholes to high crime rates and corruption.
Capriles, a centrist politician who says Brazil's free-market economics with strong welfare policies is his model for Venezuela, lost to Chavez last year by 11 percentage points. (Writing by Andrew Cawthorne; Editing by Daniel Wallis and Sandra Maler)