Some of Fine Gael's representatives want tighter travel restrictions for the Republic.
At Fine Gael's parliamentary party meeting on Wednesday night, Tánaiste Leo Varadkar gave his colleagues an update on the current Covid-19 situation.
He said the current restrictions would last until March 5 and if conditions allow, the country may move from level 5 to level 4, or level 4 with modifications, similar to the manner in which the country emerged from the first lockdown last year.
A large portion of the meeting was dedicated to discussing the new travel restrictions announced by Cabinet on Tuesday
The meeting heard it was "important to emphasise that following this week’s measures there is no silver bullet to eliminate Covid from Ireland", according to a statement released by party chair Richard Bruton.
"He told party colleagues he would not rule out any strategy to deal with the pandemic as the virus continues to present new challenges. Measures taken in the last year, including closing public houses and schools, would not have been countenanced before but action had to be taken. He said when tackling Covid, a lot of humility is required."
MEP Frances Fitzgerald reportedly spoke for around 25 minutes about her views from Europe and called on the Irish Government to adopt a zero-Covid approach.
Mr Varadkar said this policy would mean 14 days with no community transmission which would be very difficult in Ireland, as even during the summer Ireland did not experience a single day without one case of community transmission.
TDs Bernard Durkan and Ciaran Cannon, and Senator Jerry Buttimer told the meeting they also want the Government to go further with mandatory quarantine.
It's understood Mr Cannon also voiced concerns that banks are getting tougher with businesses and Finance Minister Paschal Donohoe said he would contact them.
Jerry Buttimer, who recently had the whip restored after months in exile after his attendance at the Oireachtas Golf Society dinner during the summer, was critical of the Government's failure to engage with gardaí in advance of the new rules on quarantine for returning travellers, sources say.
Mr Buttimer also took issue with leaks from the parliamentary party to the media.
Leo Varadkar said he was quietly confident a phased reopening of schools would begin next month and continue into March.