The Taoiseach has told the Cabinet that there are no indications so far that virus levels are low enough to allow any easing of restrictions on 5 May, according to a Government spokesperson.
This view was echoed by Minister for Health Simon Harris to his ministerial colleagues.
The National Public Health Emergency Team will consider the current restrictions further this Friday in advance of a Cabinet meeting later that day.
Today's meeting also included an update from Minister Harris on the progression of Covid-19 in the country, the current position on testing and tracing and the position on long-term care facilities.
It is understood that there were mixed views at Cabinet this morning around the easing of the Covid-19 restrictions.
Several ministers highlighted the need for what was termed "a little bit of give" on the restrictions.
There was concern expressed by some that an extended lockdown could lead to the permanent loss of many jobs.
It is anticipated that any easing of restrictions will be minimal and could include the opening of some smaller shops.
The Cabinet received updates on the Covid-19 crisis from Mr Varadkar, Mr Harris and Minister of State with Special Responsibility for Disability Issues Finian McGrath.
It was understood that among the issues discussed were hospital admissions, Intensive Care Unit capacity, and supports for nursing homes and other sectors.
This evening the Chief Medical Officer at the Department of Health said they are not yet in a position to recommend an easing of restrictions, saying the public "has to stay the course as much as possible".
In a two-page letter, posted on Twitter, she said disease transmission must be under control and that the Government needed "to plan to lift restrictions on an all-island basis".
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.
Additional reporting Paul Cunningham