(Adds death in Tachira, paragraphs 2 and 7)
By Andrew Cawthorne and Diego Ore
CARACAS, March 10 (Reuters) - A Chilean woman was shot dead while clearing a barricade put up by anti-government protesters, the first foreign fatality during a month of civil unrest in Venezuela, authorities said on Monday.
The deaths of Gisela Rubilar, 47, who was studying in the western Venezuelan city of Merida, and of a protester shot in the border state of Tachira, brought to at least 22 the number of fatalities in five weeks of unrest.
"She was ambushed by extreme right-wing groups ... She was vilely murdered with a shot in the eye," Alexis Ramirez, the governor of Merida state, told reporters, blaming the killing of Rubilar on unidentified demonstrators in the Andean city.
Students and militant opponents of President Nicolas Maduro have been maintaining street barricades in various cities since last month, demanding the president's resignation and solutions to problems of rampant crime and economic shortages.
The barriers have become frequent flashpoints for violence between protesters, police and government supporters.
People from both sides of the political divide, as well as members of the security forces, have been among the victims of the country's worst unrest in a decade.
Daniel Ceballos, mayor of San Cristobal in Tachira state, said on Twitter that a student, Daniel Tinoco, was shot dead there late on Monday as protesters and government supporters clashed. San Cristobal has been hardest hit by the turmoil.
In Merida, the authorities said Rubilar was a mother of four and a member of the ruling Socialist Party. A classmate told Reuters she was studying higher education, had lived in Merida for six years and worked as an artisan.
Maduro said on state television that investigations were advancing and that her killers had been identified.
"We're on their trail," he said. "Rest assured, Chile and Latin America, we are going to capture the assassins of this compatriot and they will pay for this horrendous crime."
Chilean President Sebastian Pinera said his government had asked Venezuela to provide them with all the information about the circumstances and cause of Rubilar's death.
Although street protests helped briefly topple Venezuela's late socialist leader Hugo Chavez in a botched 2002 coup, there seems little chance the current unrest could lead to a Ukraine-style overthrow of his successor, Maduro.
The military, which played a crucial role in 2002, appears firmly behind Maduro. Opposition leaders are also split between militants who back the street action and moderates who believe that tactic risks violence and lacks widespread support.
The ongoing, daily protests are a mix of peaceful demonstrations and violent exchanges between security forces and hooded protesters hurling rocks and Molotov cocktails.
Pro- and anti-government medical personnel held rival rallies in the capital on Monday.
Earlier in the day, the army said it raided a parking garage under Caracas' Altamira Square - a stronghold of opposition protests - and found a store of water, food, medicine, helmets and other equipment destined to keep the demonstrations going. Eleven people were arrested, the authorities said.
An increasingly confident-looking Maduro told supporters that the protesters had been defeated.
"We have faced a coup and neutralized it," he said.
But students are vowing to stay on the street indefinitely in what could be a protracted period of instability for Venezuela's 29 million people.
More than 1,300 have been arrested during the unrest, with 92 still behind bars, according to the government. More than 300 people have been injured during the unrest. (Additional reporting by Javier Farias in San Cristobal, Daniel Wallis and Girish Gupta in Caracas, and Fabian Cambero in Santiago; Editing by Brian Ellsworth, Tom Perry, G Crosse and Lisa Shumaker)