The vote was proposed by the mayor of Kerry, Cllr John Sheahan, and passed unanimously.
A formal letter, offering the condolences of the council, will now be issued.
Joy Few, 64, and her partner, Normand Larose, 62, both with addresses in Phoenix, Arizona, died when their pony and trap plunged into a rocky ravine, two miles from Kate Kearney’s Cottage, at about 2pm on Monday of last week.
Ms Few, a research supervisor at a hospital in Phoenix, and Mr Larose, who worked in construction in Phoenix, were on holiday with Ms Few’s daughter, Tonya Tier, and her husband, Bill Walthers, and their children, Caitlin, 15, and Gavin, 8. The family were travelling in three traps on the famous lakes-and-pony tour and were about two miles from Kate Kearney’s Cottage, at the end of the route, when the accident occurred.
A book of condolence was opened in the town hall in Killarney and hundreds of people have signed it. The mayor of Killarney, Niall Kelleher, yesterday said the book will be given to gardaí to be forwarded to the family of the deceased.
The narrow road that runs through the Gap of Dunloe has been a tourist attraction since Victorian times. It is a public road and it comes under the remit of the county council.
A decision on introducing bylaws to license jarvey carriages may be taken when the garda investigation and inquests are concluded, a council spokesman indicated yesterday. However, no such decision will be taken until then.
A small portion of the roadway is national park, and the majority is a public road, under the governance of Kerry County Council.
Supt Flor Murphy, of Killarney gardaí, said investigations into the tragedy are continuing.
He said all witnesses and potential witnesses, including the driver of the horse and trap, will be interviewed to piece together what had occurred.
The driver of the trap, a man in his 40s from Kilgarvan, jumped clear and avoided injury, but was taken to University Hospital Kerry, where he was treated for shock.
The relatives have now returned to the US with the ashes of the deceased.
A garda officer assigned to the family continues to liaise with them, Supt Murphy said.