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A 23-year-old man has been arrested on suspicion of an arson attack on a California mosque on Friday.

Carl James Dial Jr. was arrested late Friday and faces charges of committing arson, a hate crime and burglary.

The fire struck the Islamic Centre of Palm Springs at noon on Friday. 

The blaze was contained to the small building's front lobby, and no one was injured.

People at the mosque described hearing a "loud boom" and seeing flames, said Reymundo Nour, the mosque's acting imam. Although he was not present at the scene, he believes the mosque was "firebombed".

The mosque is about 75 miles (120 kilometres) from San Bernardino, where this month a married couple who federal officials say was inspired by Islamist extremists killed 14 people.

Many Muslims in Southern California have voiced their concerns about the possibility of being targets of right-wing extremists in response to the killings.

On Saturday, around 20 people - half of them armed with rifles - rallied outside a suburban Dallas mosque protesting against "Islamist violence" and "Syrian refugee resettlement".

A counter-demonstration was attended by 50 people and ended without violence.

Elsewhere, hundreds of people took part in a "United Against Racism and Hate" rally at a park in Dallas, prostesting against rising anti-Islamic activities and rhetoric.