The Free Legal Advice Centres, FLAC, say some people have been waiting up to 36 weeks for appointments at Legal Aid Board law centres.
It comes as the organisation releases its 2016 annual report and calls for an end to legal aid fees in domestic violence situations.
People who avail of legal aid pay a contribution fee of €130.
FLAC is calling for this fee to be waived for people experiencing domestic violence who are seeking safety, protection or barring orders.
Minister for Justice Charlie Flanagan said the fee is being reviewed by his Department and he expects a decision to made on the matter by the end of the year.
The minister said he wants to ensure that people have access to the law, which he regards as an essential human right.
Over 25,000 people received legal advice from volunteer lawyers in 2016.
FLAC's annual report shows that family, housing and employment law were the top queries.
Over 12,000 people called FLAC's telephone helpline, while more than 13,000 visited a local legal advice clinic, of which there are 67 countrywide.
The report noted that "excessive delays'" exist in some Legal Aid Board law centres for an initial consultation - the longest being 36 weeks in Longford, 29 weeks in Navan and Nenagh and 23 weeks in Kilkenny.
Waiting times for a second consultation also vary, with wait times of up to 49 weeks in Tallaght, for example.
The human rights organisation is calling for the Legal Aid Board to drop legal aid charges for people experiencing domestic violence and wants a review to be carried out to investigate the delays in legal aid appointments.
FLAC's chief executive said there is a huge demand on their basic information and legal advice services around the country.
Speaking on RTÉ’s Morning Ireland, Eilis Barry said last year more than 12,000 calls were made to their information line, while 13,481 visited a local legal advice clinic.
Ms Barry said 24% of queries related to family law, 8.6% constituted queries in relation to landlord or tenant scenarios followed by employment law.
In relation to delays to legal aid appointments, Ms Barry said FLAC suspect the long waiting times are due to the Legal Aid Board not being sufficiently resourced.
She said these delays mean that people cannot access and assert their rights.
Ms Barry said "legal aid is a fundamental part of the administration of justice and the rule of law, because it secures the constitutional right of access to the courts for many, and we think it's important that this is recognised in the budgetary allocation.
"There needs to be a realistic review of its budget, there needs to be investment to be able to deal with delays," she added.
