Nearly 2,600 people have been on Dublin City Council's social-housing waiting-list for at least 10 years.
According to details released under the Freedom of Information Act, there are a total of more than 17,500 on the waiting-list.
But 331 people rejected offers of social housing last year and 213 so far in 2019.
Labour Senator Aodhán Ó Ríordáin said the only solution to the long waiting lists is for councils to build significantly more houses.
He said: "The solution is State building of State housing on State land...it's as simple as that.
"The council and councils need to be given the opportunity to build housing on their own lands, to rezone it for housing, for councillors to agree to that and for the councils to be fronting up on that and leading that."