Employers' group Ibec has called for Ireland's international travel restrictions to be ended and for testing and tracing to be used in place of "ineffective" quarantine measures.
People entering Ireland from abroad currently have to quarantine themselves for 14 days upon arrival into the country.
Ibec CEO Danny McCoy said there were benefits from quarantine but there were costs too and the benefits will only accrue if the quarantine is effective.
Speaking on RTÉ's Today with Sarah McInerney, he said that filling out forms is an "ineffective quarantine".
He said the proportion of people with the virus is so small that testing and tracing would be more effective than a "crude" quarantine system.
He said the ongoing restrictions as a result of Covid-19 continue to suppress the economy and is leading to other bad health outcomes and even creating air bridges with some countries carries risks unless transmission rates are at zero in those countries.
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Mr McCoy said it is important for many businesses that travel resumes as "subject matter experts" have to fly in to serve business all the time.
Public health expert Dr Gabriel Scally said he would favour the continuation of quarantining to achieve a zero-Covid-19 Ireland.
Speaking on the same programme, Dr Scally said he doubts that anyone outside the aviation industry thinks dropping the quarantine period is a good idea and that the quarantine measures should be extended past 9 July.
The only safe way forward, he said, is to keep up the barriers and be a zero-Covid island, before opening travel links with other countries who are in a similar situation.
Dr Scally said the disease was imported by air and the country does not need a second wave when things are going well.
He said the idea of air bridges is a good one and gradually over time, as more countries eliminate the virus, more opportunities for that type of travel will open up, adding that one of the busiest air links in Europe is Dublin to London, but the situation in England is not under control.
Pádraig Ó Céidigh, aviation taskforce member and aviation businessman, said there is no way of policing quarantine and he believes that "it isn't working".
Mr Ó Céidigh said the code of practice for safe air travel, developed by the European Centre for Disease Prevention and Control, should be adopted.
The number one objective of aviation in Ireland, he said, is safe travel for passengers and this objective will remain number one.
He said that Ireland will never reach a point of becoming a zero-virus country.
Elsewhere, the Irish Congress of Trade Unions has called on the Government to make Covid-19 an occupational illness.
ICTU General Secretary Patricia King has written to the Minister for Business, Enterprise & Innovation, Heather Humphreys on the issue.
If contracting Covid-19 in the workplace was designated an occupational illness, all cases would have to be notified to the Health and Safety Authority.
"In particular healthcare workers continue to perform their duties in circumstances of serious and ever-present danger of contracting that disease. The situation in which they are, of necessity, placed is without precedent or parallel," the letter from Ms King states.
"Public transport workers frontline workers interacting with the public, airport and port workers are by virtue of the nature of their occupation also more exposed to the virus."
More than 8,000 healthcare workers have been infected with the virus, with the majority of these cases of the virus contracted in the workplace.
Additional reporting Fergal Bowers