(Adds new fatality, protest details)
By Andrew Cawthorne and Daniel Wallis
CARACAS, Feb 20 (Reuters) - Security forces and protesters fought around Venezuela on Thursday in streets blocked by burning barricades and a supporter of socialist President Nicolas Maduro was shot dead, the sixth fatality from more than a week of violence.
Maduro said a "fascist bullet" killed Alexis Martinez, a brother of a ruling Socialist Party legislator, in the central city of Barquisimeto. A local journalist said Martinez was shot in the chest while passing an opposition protest.
There have also been scores of injuries and arrests since the violence broke out eight days ago, the most serious unrest since Maduro was narrowly elected in April 2013. (For full coverage: )
The protesters, mostly students, want Maduro to resign, and blame his government for violent crime, high inflation, shortages of goods and alleged repression of opponents.
The most sustained clashes on Thursday were in the western Andean states of Tachira and Merida, which have been especially volatile since hardline opposition leaders called supporters onto the streets in early February.
In Tachira state capital San Cristobal, which some residents are describing as a "war zone," many businesses remained shut as students and police faced off again in barricaded streets.
With some residents saying they dared not leave their homes because of the violence, the government said it was taking "special measures" to restore order there.
"This is not a militarization," Interior Minister Miguel Rodriguez Torres said on state television from San Cristobal. "We are here to work for the great majority of people in Tachira. ... Before we have dialogue, we must have order."
Maduro says he will not let his rivals turn Tachira into "a Benghazi," referring to the violence-racked Libyan city.
On Wednesday night, Caracas saw one of the worst bouts of violence since the protests began nearly three weeks ago.
Around a square in the wealthier east of the city, security forces fired teargas and bullets, chasing youths who hurled Molotov cocktails and blocked roads with burning piles of trash.
'DON'T GIVE UP!'
Caracas was much calmer on Thursday, though knots of opposition demonstrators gathered again in the same square, Plaza Altamira. Some businesses stayed closed, a further drag on the already ailing economy.
The government said a funeral parade for deceased folk singer Simon Diaz, a beloved figure who died on Wednesday aged 85, was held up due to "violent groups" blocking roads.
Tensions have escalated since opposition leader Leopoldo Lopez, a 42-year-old Harvard-educated economist, turned himself in to troops this week. He is being held in Caracas' Ramo Verde military jail on charges of fomenting the violence.
"Change depends on every one of us. Don't give up!" Lopez's wife, Lilian Tintori, said on Twitter on Thursday.
Local TV channels are providing almost no live coverage of the unrest, so Venezuelans are turning to social media to swap information and images. Falsified photos are also circulating.
Both sides rolled out competing evidence of the latest violence on Thursday. Ruling Socialist Party governors showed photos and video of charred streets and torched vehicles, while the opposition posted footage of brutal behavior which they said was by National Guard troops.
Protest leaders say soldiers and pro-government armed community groups known as "colectivos" are sometimes shooting at demonstrators, while officials say sharpshooters are targeting pro-Maduro rallies from rooftops and elsewhere.
Maduro, elected last year to succeed socialist leader Hugo Chavez, says Lopez and "small fascist groups" are in league with the U.S. government and want a coup.
He has been sharply critical of international media coverage, and on Thursday he warned CNN it risked being kicked out of the country if it did not "rectify" its ways.
U.S. President Barack Obama has criticized Maduro's government for arresting protesters and urged it to focus on addressing the "legitimate grievances" of its people.
That brought a typically scathing response from Caracas. Obama's comments were "a new and gross interference" in its internal affairs, the government said in a statement.
"Independent governments and the people of the world want the U.S. government to explain why it funds, encourages and defends opposition leaders who promote violence in our country."
Street protests were the backdrop to a short-lived coup against Chavez in 2002 before military loyalists and supporters helped bring him back. There is no evidence the military, which was the decisive factor in 2002, may turn on Maduro now.
Countries around Latin America are watching closely. Political allies such as Cuba, which receives Venezuelan oil on preferential terms, have denounced an opposition "coup attempt," while other nations have called for dialogue between the two sides.
Lopez's defiant stance has won him admiration among opposition supporters frustrated by 15 years of electoral losses, first to Chavez and then to Maduro.
But detractors call him a dangerous hothead. He has frequently squabbled with fellow opposition leaders and was involved in the 2002 coup, even helping arrest a minister.
Though the majority of demonstrators have been peaceful, an increasingly prominent radical fringe has been attacking police, blocking roads and vandalizing buildings.
While the Caracas protests began in middle-class neighborhoods and are still strongest there, sporadic demonstrations have also spread to poorer areas of the city, residents say.
Rights groups say the police response has been excessive, and some detainees say they were tortured.
Venezuela's main opposition leader, Henrique Capriles, who lost to Maduro in last year's presidential election, disagrees with Lopez's street tactics but backs protesters' grievances and has condemned the government response.
"How many more deaths do they want?" he said to reporters on Thursday, urging opposition activists to avoid violence. (Additional reporting by Deisy Buitrago, Eyanir Chinea, Tomas Sarmiento and Girish Gupta in Caracas, and Daniel Trotta in Havana; Editing by Kieran Murray and Mohammad Zargham)