The Republic's tally of daily new coronavirus cases fell below 100 for a sixth day in a row yesterday.
Senior medics praised the vast majority of the public for following social distancing advice.
Recent accounts and images have shown packed beaches near Dublin as Ireland eases its lockdown restrictions.
The professor modelling the virus's spread for the state, Philip Nolan, said: "I remain hopeful that we can keep this up and keep the virus suppressed."
He said that was not based on any calculation of statistics.
"That is an expression of faith in humanity."
The Republic's rate of spread is at around 0.5 per infected person. The aim is to keep it below one to stop the virus transmitting exponentially.
The death toll rose to 1,583 yesterday after a further 12 deaths were announced by the National Public Health Emergency Team.
There were 76 new confirmed cases of the infection, bringing the total since the outbreak began in Ireland to 24,391.
Dr Ronan Glynn, deputy chief medical officer at Ireland's Department of Health, said they had experienced six consecutive days of under 100 new confirmed cases in Ireland.
"This is very positive and demonstrates the extent to which the public's actions have limited the spread of this disease."