Both the Fine Gael and Fianna Fáil parliamentary party meetings have heard concerns about changes to the vaccine rollout.
During the Fianna Fáil meeting, Education Minister Norma Foley said the National Immunisation Advisory Committee (NIAC) should explain the changes to prioritisation to teachers and other groups that won't get priority for the jabs.
Other TDs and Senators raised concerns about gardaí, childcare workers and carers.
In the Zoom chat function at the Fine Gael meeting, former Minister John Paul Phelan was critical of the approach.
The response from Tánaiste Leo Varadkar was criticised as very dismissive by some at the meeting.
The changes announced earlier this week will see the vaccine rollout switch to an age-based system once older people and vulnerable cohorts are vaccinated.
It has been sharply criticised by gardaí and teachers, who would have been prioritised under the previous profession-based list.
The Government has defended the changes, saying the rollout will now be "more efficient, more transparent and fairer".
WHO special envoy Dr David Nabarro, meanwhile, said Ireland’s new strategy “makes a lot of sense" as it should speed up the vaccine rollout.
The Government's currently expecting people aged between 18 and 64 to be vaccinated between May and July, working from oldest to youngest in ten-year age groups.
