The US State Department has said that it is providing consular assistance to Jamey Carney's family.
A State Department spokesperson told RTÉ News that the Trump administration has "no higher priority than the safety and security of Americans".
"We offer our sincerest condolences to the family and loved ones on their loss. Out of respect for their privacy during this difficult time, we have no further comment," they said.
A man who gardaí want to speak to in connection with the murder of Ms Carney in Killarney last week was arrested yesterday in the Middle East.
Gardaí investigating the murder had not sought his arrest or detention, but Garda Headquarters has been informed of the development.
Senior gardaí are unclear as to why he has been detained in Jordan.
Gardaí are continuing to investigate the circumstances that led to the death of Ms Carney.
Ms Carney - a 43-year-old US citizen who was the mother of a 13-year-old girl - was found dead in an upstairs room at her rented home on the Muckross Road last Tuesday.
Detectives have identified a person "of significant interest" in the case whom they wish to speak to a 28-year-old Jordanian man.
US Secretary of State Marco Rubio today met the Jordanian Foreign Minister Ayman Safadi at the Department of State in Washington DC.