The Health Minister claims there are signs Level 3 is working in Dublin, despite the Chief Medical Officer saying last night it is too early to tell.
The restrictions have been in place in the capital for more than three weeks with the numbers stabilising over the weekend, before an increase again in recent days.
Latest data from the Health Protection Surveillance Centre (HPSC) shows Cavan has the highest 14-day incidence rate, while every border country now has a rate of more than 100.
Health Minister Stephen Donnelly has encouraged everyone across the country to make Level 3 work, with the National Public Health Emergency Team (Nphet) due to meet on Thursday to assess whether current restrictions are adequality supressing the virus.
There has been just under 8,000 cases in the last two weeks, and the 14-day incidence rate is now 167 per 100,000 people, a rise of over 40 per cent in the past week.
Chief Medical Officer Dr Tony Holohan says Nphet would like to see some encouraging signs before they meet on Thursday.
"We will be looking at how well we believe the current measures are working. We would like to see some encouraging signs by Thursday of this week."
Nphet is also considering whether masks should be used in outdoor settings.
But Dr Ronan Glynn says a decision is not imminent.
"I think before we think about extending mask use more generally, it's really important at this point that people focus on using them appropriately," Dr Glynn said.
"I will again highlight the importance of people wearing masks where they can wear masks, as opposed to visors. Visors are an acceptable alternative for a very small proportion of our population who can't wear masks for a variety of reasons."
This comes as an emergency meeting will take place in Stormont later today on introducing Covid-19 restrictions in Northern Ireland.
A four to six week lockdown has been recommended by health officials in the North after 877 cases of the disease were detected yesterday.
If the measures are introduced, it may have a knock-on effect for border counties.