Le Matin newspaper reported online that according to information it had received a man and woman had died in an apartment building in the Servette neighbourhood at around 3am.
The Geneva prosecutor's office confirmed that cantonal police officers responded to reports of gunshots but it contradicted initial reports stating that three officers were injured in the incident.
"Arriving at the site (a building on the Rue Hoffmann) police officers found themselves in the presence of a man who aimed several gunshots at them," the chief prosecutor's office said in a statement.
"The officers returned fire and neutralized this person, who died," the statement said.
"During the exchange of gunshots, a police officer was wounded by a bullet in the face but his life is not threatened."
Officers discovered the lifeless body of a woman inside an apartment, the office said
It has launched a criminal investigation into the case.
The 20 Minutes newspaper said that according to its information a man in his 80s violently quarrelled with his partner, a woman around 20 years younger than him, before killing her.
When police arrived on the scene, the man pretended to commit suicide before firing on the officers, the newspaper said.
Geneva cantonal police earlier confirmed that officers made a major “intervention” on Tuesday morning and referred questions to justice authorities.
A resident of the building involved told 20 Minutes he “heard several gunshots and the cries of a woman” before police quickly arrived.
“I was woken by cries then very violent sounds, maybe gunshots,” a neighbour told the daily.
“I later saw heavily armed officers mount the stairs.”