Phoenix Police Sergeant Tommy Thompson said the shooting erupted after a morning meeting involving a legal dispute, and police were looking for a 70-year-old suspected gunman described as "armed and dangerous."
"He was involved in some type of litigation meeting," Thompson told a news conference of the suspect, giving his name as Arthur Douglas Harmon. "After that meeting, he got into an altercation with some of the individuals and actually shot two of those individuals."
Police said a third person, described as a witness who followed the gunman as he fled the scene, was also shot.
The shooting comes as the United States is on edge about gun violence after a gunman shot and killed 20 children and six adults at a Connecticut school in December, sparking a heated national debate over gun control.
It also coincided with the start of U.S. Senate Judiciary Committee hearings in Washington on possible gun control measures.
Police in Phoenix said that Steve Singer, 48, was killed and another man was in critical condition. A 32-year-old woman was being treated for a non-life threatening injury.
Two other people were taken to hospital for "stress related symptoms," although there were no immediate details of their condition.
Law firm Osborn Maledon confirmed that litigator Mark Hummels - who is president of the Federal Bar Association's Phoenix chapter - had been shot during a mediation meeting at the office building.
"Our partner, Mark Hummels, was representing a client in a mediation today when he was shot. We understand that other people also were injured," the firm said in a statement.
Hummels' practice focuses on business disputes, real estate litigation and legal malpractice defence, according to the firm's website.
Police later surrounded a house that local television news reported belonged to Harmon. He was not believed to be at the home, and remains at large.
Frank Kirby, a financial planner who works in an office near the scene of the shooting, told Reuters he was outside his building immediately after the incident and heard the gunman fire at someone in a white car.
That person then sped away in reverse as he sought to escape the gunfire, Kirby said, adding he was close enough to smell the gunpowder in the air.