By David Bailey

MINNEAPOLIS (Reuters) - Two company officials battled a worker they had just fired for tardiness and poor performance when he embarked upon a shooting rampage that killed five people and wounded three at a Minneapolis sign manufacturer last week, police said on Monday.

Minneapolis police on Monday released more details about the investigation into Andrew Engeldinger's shooting spree at Accent Signage Systems Inc. on Thursday, the worst work-place shooting on record in Minnesota.

Witnesses had provided conflicting reports to police, who said initially that Engeldinger had been fired earlier in the day and returned to the business, located in a tree-lined residential neighborhood of Minneapolis.

Police said they hoped to complete the investigation this week.

Engeldinger, 36, had been warned the previous week that he would be fired if he did not improve his performance, when he was summoned to an executive's office after an otherwise uneventful work shift on Thursday, police said.

The owner of two Glock 9mm handguns he bought legally last year, Engeldinger went to his car and then to the office to meet with executives John Souter and Rami Cooks, police said.

After they told him he had been terminated and gave him his final paycheck, Engeldinger pulled out a handgun and the three men struggled over the weapon, police said.

Engeldinger shot Cooks, who was pronounced dead later Thursday at an area hospital, and Souter, who remained hospitalized on Monday in serious condition.

Engeldinger dropped a partly loaded clip in the struggle and stopped to reload before leaving the office, police said.

At that point, Accent Signage founder and owner Reuven Rahamim stepped from his adjacent office and was shot and killed by Engeldinger, who then left the offices, police said.

Engeldinger entered an area where sales staff members had desks and displays, where he killed Jacob Beneke, police said.

From there, Engeldinger killed Ron Edberg in the loading dock area and UPS driver Keith Basinski, who was standing in his truck at the end of the loading dock, police said.

Engeldinger walked from there to a production area where he shot and wounded production manager Eric Rivers, who remains hospitalized in critical condition, and grazed a person who was treated and released.

A second Glock 9mm handgun was found in a search at Engeldinger's house after the shooting along with packaging for 10,000 rounds of ammunition, police said.

The Minneapolis shooting was a month after a work-related shooting near the Empire State Building in New York, which killed two people and wounded nine.

That followed a July mass shooting in a crowded cinema in Colorado and an attack on a Sikh temple in Wisconsin in August.

Nationally, there were 458 workplace homicides in 2011 and 518 in 2010, according to U.S. Bureau of Labor Statistics data. (Reporting by David Bailey; editing by Greg McCune and Todd Eastham)