A meeting between ministers and the National Public Health Emergency Team (NPHET) could be held as soon as next week to facilitate discussions on the Covid-19 physical distancing rule of people remaining two metres apart.
It is understood that there was a "robust" discussion on the issue at Cabinet today.
Some ministers were advocating the adoption of World Health Organization guidance, which states that a one-metre distance is considered to be safe.
Advocates of such a change argued that it would have a very positive impact for both small businesses and schools.
It is believed that after the debate, Taoiseach Leo Varadkar suggested he would try to arrange a meeting between the seven or eight ministers backing the proposal and Chief Medical Officer Dr Tony Holohan and his team.
Fianna Fáil health spokesperson Stephen Donnelly said: "Reducing the required distance from two metres to one metre would clearly make things a lot easier for many people, and services like education, healthcare and work.
"We must be led by the public health advice on this, and if the CMO, after consultation with the NPHET, believes that one metre is now acceptable, then we should implement that with all haste."
Labour leader Alan Kelly said: "After the complete confusion over the bonkers two-hour rule this week, we now need a clear explanation from the Government on why we are specifically using the two-metre rule and if the WHO is recommending that distance.
"Otherwise it would make life much easier for society and businesses if we, like the rest of the EU, were using the one-metre rule, if that was possible."
On the new international travel regulations, Cabinet is said to have been very supportive of the proposals from Minister for Health Simon Harris.