The young woman who was stabbed to death in Dundalk on Tuesday afternoon was named Ingrida Maciokaite.
Ingrida, 31, originally from Lithuania, was killed in a brutal attack around 14.45 at the Bridgewater Mews apartment complex on Linenhall Street in the city.
One source said: "It is assumed that a quarrel broke out and the woman sustained serious stab wounds.
"Medics and gardai rushed to the scene, but they could not save her."
A man, in his forties and also from Lithuania, was arrested shortly afterwards and interrogated by detectives in Dundalk.
Gardai started an investigation and closed the apartment block in Linen Hall Street in the city.
It is assumed that the victim and the man have been living in the general Dundalk area for a while.
Cllr Liam Reilly said he was shocked to hear about the incident.
He added: "I would like to express my deepest sympathy to the dead woman's family."
A Garda spokesman said the man was arrested on suspicion of an attack and after a post-mortem examination could be upgraded.
A statement from Garda adds: "The scene is kept for a technical and forensic investigation and an emergency room has been set up." The pathologist-pathologist and coroner's office has been informed.
"A man in his forties has been arrested in connection with this investigation and is currently being detained at the Dundalk Garda station.
"Research is continuing."