A man was shot Monday as a heavily armed militia group attempted to defend a statue from US protestors in New Mexico, officials and media reports said.

Monuments linked to colonialism and slavery are being toppled and removed globally as worldwide anti-racism protests continue after the death in US police custody of George Floyd, an unarmed black man.

Albuquerque city protesters were demanding the removal of a statue of the state's 16th-century governor, Spanish conquistador Juan de Onate, according to local media.

As they tried to pull down the sculpture, a small group of right-wing militia members tried to protect it and clashes erupted, the Albuquerque Journal reported.

The victim is believed to be in a critical but stable condition, police said.

Police were investigating reports "about vigilante groups possibly instigating this violence," city police chief Michael Geier said in a Twitter statement.

"If this is true will be holding them accountable to the fullest extent of the law, including federal hate group designation and prosecution," he said.

Images in US media showed police apprehending a number of men, some dressed in camouflage gear with guns.

"The heavily armed individuals who flaunted themselves at the protest, calling themselves a 'civil guard', were there for one reason: To menace protesters, to present an unsanctioned show of unregulated force," said New Mexico Governor Michelle Lujan Grisham said in a statement posted on Twitter.

"Let me (be) clear: There is absolutely no space in New Mexico for any violent would-be 'militia' seeking to terrorize New Mexicans," she added.

Albuquerque's Mayor Tim Keller said on Twitter that the statue had been temporarily removed to contain the risk to public safety.