Acting Chief Medical Officer Dr Ronan Glynn has said that the pandemic appears to be accelerating once again across Europe, but that "we have an opportunity to avoid a similar scenario here".
This evening, the Department of Health said it had been notified of no new deaths and 14 additional confirmed cases.
There have been a total of 1,764 Covid-19 related deaths in Ireland, and 25,942 confirmed cases.
Dr Glynn said that 11 of today's cases were close contacts of confirmed cases and half of these had no symptoms.
He added: "If you are concerned that you have been in contact with a confirmed case please come forward for testing. Do not wait for symptoms to emerge."
He said there are now eight confirmed cases of Covid-19 in the hospital system, the lowest number since early March.
Highlighting the increase in cases in Europe, he said people must focus once again "on keeping our distance, washing our hands, wearing face coverings and continuing to make safe decisions that will protect ourselves, our friends, our families. No one is safe unless everyone is safe."
In Northern Ireland, the Department of Health has confirmed that there have been no further deaths from Covid-19 reported in the past 24 hours.
It means that Northern Ireland has now recorded no coronavirus-related deaths for 16 consecutive days.
The death toll there since the beginning of the pandemic remains at 556.
Nine new cases of the disease have been identified, taking the total to 5,930.
There are five confirmed Covid-19 patients in Northern Ireland hospitals, with two being treated in ICU.
Meanwhile, people in the Republic on the Pandemic Unemployment Payment who travel to green list countries will continue to receive their payments.
Minister for Social Protection Heather Humphreys told the Dáil that the cases of all those who travelled for holidays and were penalised will be reviewed.
The issue has continued to cause controversy in recent days with the legal rights agency, FLAC, stating that there was "no clear legal basis" for the sanctions on PUP recipients.
Taoiseach Micheál Martin said that more than 2,000 people in receipt of the payment have had their cases closed as a result of checks carried out at Dublin Airport.
But he said the vast majority of these claims relate to people who have been leaving the country on a permanent basis.
We had 14 new cases of #COVID19 confirmed. No fatalities, thankfully.— Stephen Donnelly (@DonnellyStephen) July 29, 2020
8 people are in hospital with complications of Covid, lowest we have seen since March.
The situation is worsening in some other parts of Europe, which we're monitoring closely. #holdfirm
Elsewhere, deaths from Covid-19 in the United States have surged to their highest level in months.
According to the latest Reuters tally, 10,000 coronavirus deaths have been recorded in 11 days as the number of fatalities surpassed 150,000.
Case numbers have been rising for weeks across large parts of the country.
As the search for a vaccine continues, the European Commission has ordered 30,000 treatment doses of the antiviral medication remdesivir from US drugs giant Gilead.
Sold under the brand name Veklury, remdesivir is the first medicine to be approved by the EU to treat victims of the pandemic in EU member states and in Britain.
It is hoped the drug will shorten recovery times for patients with severe infections and it will be made available early next month.
In Russia, President Vladimir Putin has said the country's coronavirus outbreak had stabilised but warned the situation remained difficult and could easily deteriorate.
Russia has registered the fourth-highest number of infections in the world and health officials reported a total of 828,990 cases and 13,673 fatalities.