CARACAS (Reuters) - The death toll in Venezuela's six-week wave of anti-government unrest has risen to at least 42, according to the state prosecutor's office, which announced three deaths on Tuesday.

A policeman was arrested for his alleged role in the killing of a 33-year-old taxi driver, shot in the thorax, in the border state of Tachira. A 17-year-old who was shot in the head during a protest in the central state of Barinas on Monday and died on Tuesday morning.

"A group of people arrived and started shooting, injuring the young person in the brain," the state prosecutor's office said on the death of the unnamed teenager.

Another person, whose name and age were not disclosed, died in protests in San Antonio, according to authorities.

Violence flared in various parts of the country on Monday as the opposition held sit-ins and roadblocks, trying to keep up momentum in its bid to remove the socialist government.

Hundreds of thousands of people have taken to the streets in recent weeks, angry about food shortages, a medical crisis and soaring inflation. Protesters are demanding elections, freedom for jailed activists, foreign aid to offset an economic crisis, and autonomy for the opposition-controlled legislature.

President Nicolas Maduro blames the opposition for the country's crisis and the deaths, which have occurred on all sides. He accuses his opponents of trying to oust him in a coup with the backing of Washington.

At least 90 people were arrested during Monday's unrest, according to a local rights group.

The United Nations Security Council is due to meet behind closed doors regarding Venezuela on Wednesday at the request of the United States, diplomats said. It will be the first time the 15-member body has discussed the crisis.

Graphic on Venezuela’s economic woes: http://tmsnrt.rs/2pPJdRb

(Reporting by Girish Gupta and Corina Pons; Editing by Lisa Von Ahn and Andrew Hay)