CARACAS (Reuters) - A wave of lootings and food riots in crisis-hit Venezuela has left three people dead in the last week, authorities and a rights group said.

The state prosecutor's office is investigating the deaths of a 21-year-old man in eastern Sucre state on Saturday, another 21-year-old man in the Caracas slum of Petare on Thursday, and a 42-year-old woman in the western state of Tachira last Monday.

All three were shot during chaotic protests and melees outside shops, which have become flashpoints for violence and looting amid scarcities of basics across the South American OPEC member country, according to local rights group Provea.

A policeman has been arrested over the Tachira death.

And a National Guard sergeant major was arrested for the shooting in Sucre, the prosecutor's office said on Monday.

With basics such as flour and rice running short, crowds chanting "We want food!" are thronging supermarkets daily, presenting a major problem for the struggling leftist government of President Nicolas Maduro.

More than 10 incidents of looting are occurring daily, according to the Venezuelan Observatory of Violence, a local monitoring group.

Venezuela's political opposition is pursuing a recall referendum in an effort to remove Maduro, a socialist, from office.

Maduro, 53, who won election to succeed Hugo Chavez in 2013, accuses foes of deliberately stirring up trouble and seeking a coup.

(Reporting by Sarah Dagher, Girish Gupta and Diego Ore; Editing by Andrew Cawthorne, G Crosse)