(Adds Supreme Court, protest in Caracas, Air Canada; edits)
By Daniel Wallis and Diego Ore
CARACAS, March 17 (Reuters) - A Venezuela National Guard captain died on Monday after being shot in the head during a demonstration, the military said, the 29th fatality in six weeks of clashes between protesters and security forces.
General Padrino Lopez, head of the armed forces' strategic operational command, said the captain was shot late on Sunday at a street barricade set up by demonstrators in the central city of Maracay, in Aragua state.
"He was another victim of terrorist violence," Lopez said on Twitter, calling for an end to the confrontations. "Our armed forces don't repress peaceful protests, they protect them."
Since early February, students and hardline opposition leaders have been calling supporters onto the streets to protest against President Nicolas Maduro and his socialist government.
The demonstrators are demanding political change and an end to high inflation, shortages of basic foods and one of the worst rates of violent crime in the world.
The protests, however, show no signs of toppling Maduro, a 51-year-old former bus driver who narrowly won an election in April 2013 to replace his late friend and mentor, Hugo Chavez.
Tareck El Aissami, governor of Aragua state and a member of the ruling Socialist Party, said authorities arrested a "Chinese mercenary" near where the National Guard captain was killed.
Aissami said an "arsenal" was found in the man's home, and showed video of hundreds of rounds of different calibers.
He gave the man's Venezuelan identity card number, but did not elaborate further. The government has often talked of alleged assassination plans, but rarely provides many details.
In the western border state of Tachira, which has been hardest hit by the violence, residents rebuilt some barricades overnight on streets that the authorities had cleared.
In Puerto Ordaz, in the south of the country, Reuters witnesses said riot police clashed with hundreds of students. At least two government-owned vehicles were burnt by protesters.
COURT ORDERS BARRICADES DOWN
On Monday, the Supreme Court ordered the opposition mayors of four municipalities to remove street barricades set up by demonstrators. It issued a similar order against two opposition-run municipalities in eastern Caracas last week.
It also summoned the opposition mayor of a municipality in central Carabobo state to explain his "presumed failure" to comply with another order to remove barriers from roads.
The opposition Popular Will party said it was planning a march in Caracas on Tuesday to mark a month since its hardline leader, Leopoldo Lopez, handed himself in to face charges of fomenting unrest after helping kick off the demonstrations.
The protesters are far fewer than those who took to the streets a decade ago to oust Chavez, albeit briefly. Opposition leaders are deeply divided over the current confrontations.
During the daytime, thousands of opposition supporters have marched peacefully. Then a masked hard core has been emerging in the evenings, especially in wealthier eastern Caracas, to fight running battles with riot police and the National Guard.
Supporters of both political camps, and several members of the security forces, have been killed. Hundreds of people have been injured, and more than 1,500 have been arrested.
About 100 people remain behind bars, including 21 security officials accused of crimes ranging from brutality to homicide.
Air Canada said on Monday it was suspending flights to Caracas until further notice because of the unrest, saying it could not ensure the safety of its operation.
In the capital on Sunday, troops cleared demonstrators from Plaza Altamira, a square in the wealthy east of the capital that became the wreckage-strewn site of daily violent clashes.
National Guard soldiers posted around the plaza said they had seized home-made shields, materials for Molotov cocktails, and medicines used by the protesters to counteract tear gas.
Late on Monday, hundreds of protesters demonstrated peacefully in the square - in sharp contrast to previous nights' confrontations - singing and waving flags as police looked on.
Cenaida Pavon, a 40-year-old secretary walking through the square, said she supported the demonstrators' right to protest peacefully but not the destruction of property.
"They hate what President Chavez left behind," she said, adding that the nearby school her 8-year-old son went to had been closed since the start of the demonstrations.
"That's terrorism, not protest," Pavon said. (Additional reporting by Eyanir Chinea in Caracas, Javier Faria in San Cristobal, and German Dam in Puerto Ordaz; Editing by James Dalgleish and Eric Walsh)