There has been a sharp decrease in coronavirus daily growth rates in the Republic of Ireland, down from 33% at the start of the crisis to 15%, the latest figures show.
But medical authorities are warning it is too early to be complacent.
There have now been 54 Covid-19-related deaths in the country, with 2,910 confirmed cases.
It would take time to see the "impact of our efforts" in the numbers, said a senior government adviser.
It could take 10 days before there is a reliable picture, said Prof Philip Nolan, chairman of the National Public Health Emergency Team's epidemiology advisor group.
The Irish government has taken a number of steps to slow the spread of the virus.
On 12 March schools, colleges and other public facilities in the country were closed.
Then, on Friday, people were told they should only leave home for work if it is essential, to shop for essential supplies, to care for the vulnerable or to exercise.
Mr Varadkar said all non essential indoor visits should be avoided and any outdoor gatherings should include no more than four people, unless they were from the same household.
Theatres, playgrounds, clubs and gyms have been shut and hotels will stay open only for non social and non-tourist reasons.
The latest figures showed there were eight new coronavirus-linked deaths by Monday; six of those who died had an underlying medical condition and the median age was 86.
In his St Patrick’s night address to the nation earlier this month, Taoiseach (Irish PM) Leo Varadkar suggested there could be up to 15,000 cases by the start of April - five times more than the number confirmed so far.
Of the confirmed cases, 50% of patients are male, the median age is 47 and 645 patients (26%), have been taken to hospital - 84 of whom have been admitted to Intensive Care Units (ICU).
Some 578 cases are associated with healthcare workers.
Of those for whom transmission status is known:
- Community transmission accounts for 50%
- Close contact accounts for 27%
- Travel abroad accounts for 23%
“We are beginning to see encouraging signs in our efforts to flatten the curve," said the Irish Chief Medical Officer, Dr Tony Holohan.
"However, we cannot become complacent as we are still seeing new cases and more ICU admissions every day.
"Our strategy remains the implementation of public health restrictions to interrupt the spread of the virus and prevent people from arriving to ICU in first place.”
Meanwhile, Mr Varadkar has thanked the Chinese people for their assistance in providing medical equipment to deal with the Covid-19 crisis.
In a telephone call with the Chinese Prime Minister Li Keqiang, Mr Varadkar offered to provide Irish expertise in such areas as research to the authorities in Beijing.
On Sunday, medical supplies arrived in Dublin from China - more are expected.
Premier Li said his govt would continue "to facilitate smooth implementation of these arrangements, including transport of the medical supplies to Ireland."