A government official has warned about "significant numbers" of people congregating at funerals and graveyards.
Senior civil servant Liz Canavan said there are concerns about people dropping their guard at funerals, particularly when daily coronavirus counts are so high.
Under current restrictions, funerals are limited to 10 mourners.
Ms Canavan, assistant secretary-general at the Department of the Taoiseach, said attendance at churches and graveyards is restricted to families.
She added: "Everyone is finding the restrictions difficult and they become even more difficult when they interrupt our ability to say goodbye to those who love.
"We aren't able to give people the send off that they deserve.
"Priority has to be given to families themselves that attend funerals, whether this is in the homes of the deceased, or in the funeral home.
"In this third wave we now sadly see a significant increase in the number of funerals. Concerns are being raised regarding the dangers of dropping our guard at funerals when we're at this critical time.
"Reports of significant numbers of people congregating in the homes of bereaved persons and in funeral homes, or at churches and graveyards, before and after services are concerning.
"The inclement weather we have this time of year can also result in those lining funeral routes at times congregating in doorways of churches and other areas along the route to seek shelter."
She warned that every contact increases the risk of transmission of the virus.
She urged anyone wishing to express their condolences to do so through social media sites, websites or by sending a text message or sympathy card.
"It is vital that, despite our natural emotions and our desire to be close to and hug other people, to respect the situation we find ourselves in as we try to convey our sympathies to bereaved families.
"It is important to remember our objective to reduce the spread of the virus and we should all do what is right, even if it is difficult and different."
During the government's briefing on Covid-19, Ms Canavan also said the Department of Social protection issued payments this week to more than 475,000 people in receipt of Pandemic Unemployment Payment (PUP).
"This payment is valued as 142.86 million and marks a 3% increase on last week," she added.
"These figures are in addition to 189,860 people who are on the live register at the end of December.
"The lowest number of people claiming PUP was on 21 December at 277,700. That's a 200,000 increase in one month."
