San Francisco police arrested a 27-year-old man on suspicion of attempted murder after a woman was stabbed early Christmas morning in San Francisco.

Investigators were working to determine if the incident was related to another stabbing earlier in the night that killed a 70-year-old woman, said Officer Robert Rueca, a San Francisco police spokesman.

Michael Jacobs, a homeless man, was arrested after the second stabbing, which happened around 12:40 a.m. Tuesday at Third and Market streets, Rueca said. The victim, a 43-year-old woman, was taken to a hospital with life-threatening stab wounds.

Police were called at about 5:30 p.m. Monday to Jessie Street between Sixth and Mint streets, where they found the 70-year-old woman suffering from apparent stab wounds. Paramedics pronounced her dead at the scene.

Homicide investigators are trying to determine if the crimes are connected because “both of these crimes involved stabbings that occurred within close proximity to each other,” police said in a statement.

Anyone with information on the stabbings can call the Police Department’s tip line at 415-575-4444 or send a text message to TIP411 beginning with the word “SFPD.”

The back-to-back stabbings come amid a sharp decline in violent crime in the city. San Francisco has recorded 46 killings so far this year.

Kimberly Veklerov is a San Francisco Chronicle staff writer. Email: kvekler ov@sfchronicle.com Twitter: @kveklerov