Only a minority of Travellers have not adhered to public health guidance in relation to Covid-19 and the majority of the community have been "exemplary", a co-director of Pavee Pointhas said.
Ronnie Fay told RTÉ's Morning Ireland that the orgnaisation does not condone breaches of the guidelines and said it is "unacceptable" to have large gatherings throughout the pandemic.
However, she said that the spotlight focuses on large attendances at one event like a funeral or wedding and that stigmatises and vilifies the entire Traveller population.
Ms Fay said that some Travellers have not attended their children's weddings and grandparents have not seen their grandchildren for some time.
She said that the numbers of cases of the virus are high in the Traveller community and people need to recognise the large health inequalities that they faced prior to Covid-19, with mortality rates four times the national average.
She said that a person's living environment affects the opportunity to protect against Covid-19 and many Travellers live in large family environments that are overcrowded with poor living conditions.
Ms Fay said that older Travellers have had access to vaccination and the rollout of vaccines is now being planned for the whole Traveller community.
She said a very pragmatic approach to administering the vaccine is needed, through GPs or mass vaccination clinics, but in some areas outreach or pop-up clinics may be required.
She said that the Health Service Executive has been very collaborative in their approach to Covid-19 in the Traveller community and the overall joined-up thinking of Government and Traveller organisations shows what is possible.
She said that post-Covid this should continue and lead to proper resourcing of the National Traveller Health Action Plan.
The Cathaoirleach of Longford County Council Paul Ross said he accepts people are angry and annoyed over yesterday's incident in relation to a gathering of 100 people for a wedding, but he believes the council did all it could to try and to stop the event.
He said the local authority became the first in the country to seek a court order to stop a mass gathering and to see the event going ahead "was a big blow".
Gardaí said today that they attended the scene and will enforce breaches of Covid-19 regulations detected and in particular current travel restrictions.
A file is now being prepared for the DPP.
Co-Director of Pavee Point Martin Collins said large gatherings at this time are "not acceptable" and he's urged members of the travelling community to follow the guidelines.
"I’m pleading with you. Please be more responsible and respect the public health guidelines. This is about saving lives at the end of the day" he said.
Mr Collins said most travellers are obeying the regulations and he said it is only a "small number of travellers" who are not obeying the guidelines, "just like some members of the settled community" are not following the guidelines.
The comments come in the wake of an investigation after a wedding celebration with up to 200 people in a marquee on Longford County Council property. The marquee was set up next to a halting site.
It is understood that gardaí spoke to the organisers of the event on Tuesday and made them aware of the Covid-19 restrictions with regard to staging an event of this nature.
Yesterday morning, Longford County Council sought and received an emergency court order to prevent the event going ahead.
However, following the wedding ceremony at St Mel's Cathedral in the town yesterday afternoon, a group of 100 people arrived at the location and entered the marquee.
Gardaí said they were at the scene to support the local authority in serving the court order.
However, when the county council and its agents left the area, gardaí also withdrew and it is understood that up to 200 people attended the event.
Gardaí say they will carry out interviews with witnesses and prepare a file for the DPP.
Additional reporting Ciaran Mullooly