About 3.30pm on Monday, Riverina Police District officers were patrolling Beckwith Street when they observed a man wanted on outstanding warrants travelling in a purple Daihatsu Charade.

In a statement, police said officers gestured for the vehicle to stop, and when the driver allegedly failed to comply a pursuit was initiated.

"Shortly after, the vehicle allegedly collided with two other vehicles at the intersection of Darlow and Docker street.," the statement read.

"The man fled on foot and was arrested shortly after. The vehicle continued to travel along South Parade before a woman allegedly exited the vehicle and fled on foot."

Police said the driver of the vehicle, a 22-year-old woman, was arrested on South Parade.

A backpack containing a firearm and ammunition was located in the backyard of a nearby residence.

The 34-year-old man was charged with possessing a shortened firearm, giving a shortened firearm to other, possessing ammunition, not keeping a firearm safely and acquiring firearm subject to a prohibition order.

He was refused bail and is due to re-appear at Wagga Local Court on January 7.

The 22-year-old woman was charged with two counts of not giving particulars to another driver, using offensive weapon to prevent lawful detention and police pursuit.

She was granted strict conditional bail to appear before Wagga Local Court on November 26.

Riverina Police District's Adrian Telfer said police had been searching for the man on an outstanding warrant.

"Yesterday at 3.30pm, police sighted a motor vehicle in central Wagga and made attempts to stop that vehicle," he said.

"Unfortunately a pursuit followed that, and ended down in the vicinity of Docker Street and South Parade."

Inspector Telfer said the incident ended without anyone getting hurt.

"We are putting serious allegations before the court, and thankfully this is one other firearm that is off the street," he said.