The number of homeless children in Dublin has more than doubled in a year, the latest figures show.
They also show the total number of homeless people during the week of September 21st to 27th was 4,999.
This was made up of 1,571 children, 980 parents and 2,448 adults without children.
Asked about the issue during the Fine Gael presidential dinner at the Double Tree by Hilton hotel in Dublin on Saturday night, Mr Kenny said he had sat with a homeless man for 20 minutes earlier in the day and listened to his story.
The Taoiseach said many people would be sleeping rough on the streets that night and claimed a recovering economy would be the “engine” that will help solve the homelessness crisis.
In January, the total number of homeless persons was 3,845 - 865 children, 539 parents and 2,441 adults with no dependents.
The national data, just published by the Department of the Environment, show there were 1,571 homeless children in 738 families across the State last month.
This is an 81 per cent increase in the number of homeless children since January, when there were 865 children in 401 families.
The highest numbers of children were in Dublin, where there were 1,343 in 637 families in emergency accommodation last month.
This compares to 668 homeless children in 309 families in September 2014 - meaning a 101 per cent increase in the number of children, and 106 per cent increase in families, in emergency accommodation in the capital in a year.
Outside Dublin, there were 228 children in 101 families in emergency accommodation last month, compared to 85 children in 42 families in January.
The use of commercial hotels for emergency accommodation for families also continues to increase in Dublin, as supported emergency accommodation (ie intended for that purpose) runs at full capacity.
The number of families in hotels in Dublin has increased from 216 in January to 401 last month - an 86 per cent increase.
The figures show the number of homeless children has risen steadily across the State since the start of the year, though the numbers outside Dublin continue to rise at a percentage rate more than twice that found in the capital.
While the number of homeless children in Dublin has risen by 72 per cent since January, from 780 to 1,343, the increase outside Dublin has been 167 per cent, from 85 at the start of 2015 to 227 last month.
The biggest increases in the number of homeless children have been in the commuter areas outside Dublin, with the mideast and southeast regions showing increases of 333 per cent (from 12 to 52) and 1,400 per cent (two to 30) respectively since January.
A further continuing trend is the preponderance of single parents with children among the homeless family statistics.
In Dublin, of the 637 families in homelessness accommodation last month, 419 (65 per cent) were headed by single parents.
Outside Dublin, of the 101 families, 77 (76 per cent) were headed by single parents.
Of the 2,448 homeless single adults without children in emergency accommodation across the State, 1,475 of them were in Dublin and 973 outside Dublin.