The Minister for Health Simon Harris has said the reproductive rate of the coronavirus has remained stable at around 0.5.
Speaking in the Dáil, Minister Harris said the number is now between 0.45 and 0.63.
He said for four weeks in a row the number has remained significantly below one.
The Minister said the sacrifices that have been made have pushed Covid-19 back, but he said, it has not gone away.
Professor Philip Nolan, the Chair of the NPHET Irish Epidemiological Modelling Advisory Group will outline the latest projections and calculations related to the virus this evening.
A reproduction rate of 0.5 for the virus means that if ten people become infected with Covid-19, as things stand now, they are likely to pass the virus on to five other people between them.
Then those other five people will in turn pass it on to two and a half additional people and so on, in an every declining cycle of infection until the virus would eventually burn itself out in the community.
However, the easing of social restrictions on Monday last has resulted in significant additional mobility among the population.
There are fears that this will cause the reproduction rate of the virus to rise and increase the rate of infection and spread of Covid-19 in the community.
It is too soon however, to measure the impact of the first round of easing of restrictions on the reproduction rate because it takes longer than three days for symptoms of the virus to manifest themselves in newly infected people.
The Government has allowed three weeks in between each of the five stages of the roadmap for lifting the social, travel and work restrictions in order to gauge the impact on the spread of the virus before proceeding to the next stage.
Earlier, the Deputy Chief Medical Officer has said that if there is a second wave of Covid-19, the country will know which measures to take.
Dr Ronan Glynn said we will have to live with the virus for the foreseeable future, but the measures taken here show that it can be controlled.
Speaking at the Department of Health briefing last night, Dr Glynn was asked about the possibility of a "second wave" of Covid-19 later this year.
He said: "There's no doubt that we will have to live with this virus for the forseeable future.
"We don't have a vaccine, we don't have a treatment and we have one type of test as things currently stand."
He added: "It is a challenge but we have seen with the measures we've taken that we can control it.
"I would not like the message to go out that there's nothing we can do as a population to control this.
"But I would be confident that if things do go in the wrong direction, that we know what measures to take."
Dr Glynn also confirmed that four members of the Roma community in Ireland have died following a Covid-19 diagnosis.
In total, 22 people form the Roma community have been diagnosed and seven hospitalised.
There have been 19 cases of the virus in prisons, with two people hospitalised.
There were 46 cases among members of the travelling community, with two hospitalised.
The Department of Health said 171 people living in direct provision were diagnosed with Covid-19 and 14 people admitted to hospital.
There have been 20 cases among the homeless community, with five people hospitalised.
Dr Glynn said the message to employers is to limit employees coming to the workplace as much as possible.
He said all sectors of society have to weigh up the risk and benefit of each situation.
"There's no relaxation of measures that doesn't result in at least some level of increased risk," he added.
Yesterday, the Department of Health said a further 11 people with Covid-19 had died in Ireland bringing the overall death toll to 1,571.
An additional 64 more cases of the coronavirus have been diagnosed bringing the number of confirmed cases to 24,315.
The Principal Expert for Emergency Preparedness and Response with the European Centre for Disease Control has said most European countries are passing, or have passed, the peak of Covid-19.
Speaking on RTÉ's Morning Ireland, Agoritsa Baka warned that this does not mean the virus is gone.
The ECDC is preparing a risk assessment for the arrival of a second wave, she said, adding that it is not a question of 'if’, but ‘when’ this will happen.
Ms Baka said Ireland has done "remarkably well" in dealing with the virus.
Around 80% of cases of Covid-19 will be a mild to moderate illness, close to 14% have severe disease and around 6% are critical.
Generally, you need to be 15 minutes or more in the vicinity of an infected person and within 2 metres of them, to be considered at-risk, or a close contact.
There are now almost five million coronavirus cases worldwide, less than two weeks after the world hit the four million mark.
Yesterday saw the biggest one-day rise in infections since the pandemic began, with 106,000 new cases.
The WHO has expressed concern about rising infections in low and middle-income countries.
Reporting: Sinéad Crowley, George Lee, Aisling Kenny