Zabani Khachukayeva is nine years older than Japanese woman Kamato Hongo, 115, the oldest living person whose date of birth has been authenticated by the Guinness Book of Records.
Khachukayeva, from the small mountainous republic's southwestern Achkoy-Martan district, has 24 grandchildren, 38 great-grandchildren and seven great-great-grandchildren.
She had six children, four of whom died at an early age.
Her oldest son, Akhdan, died two years ago and is survived by his 14 children.
Doctors who have examined Khachukayeva said she is in good health for her age.
Her only complaint is that she has had problems with her hearing over the past couple of years.
Despite her advanced age, she still works around the house, looks after her numerous great-grandchildren and great-great-grandchildren, and prays five times a day.
- Jeanne Calment, the oldest ever woman, died aged 122
- Current record holder Kamato Hongo is 114 years, 183 days
The Russian authorities have several times in recent years announced a new record for the world's oldest person, but none have been authenticated.
In January 2001, the republic of Dagestan reported the world's oldest man, 134-year-old Gayirkhan Iriskhanov, lived in a local village.
Then a Russian census last year found that a 116-year-old Siberian woman Pelageya Zakurdayeva, born on June 6, 1886, was believed to be the longest-living person in the world.
However, the current title-holder, Kamato Hongo, took the honour aged 114 years 183 days on the death of American woman Maude Farris-Luse, who died in March 2002.
Luse reportedly credited an intake of boiled dandelion greens and fried fish as the reason for her long life.
Jeanne Louise Calment, the oldest ever woman to be authenticated by the Guinness Book of Records died in France in 1997, aged 122.