Tanaiste Leo Varadkar has intervened to warn TDs and senators they will be expelled if they do not support Government legislation.
Varadkar also told the Sunday Independent the three governing parties will have to "do things differently" when they return after the summer.
"The last few weeks were chaotic," the Fine Gael leader admitted yesterday. "I think all three parties are going to have to do things differently in September and communicate better with each other and our own."
Varadkar's comments follow the Green Party's sanctioning of two TDs after they did not vote with the Government on legislation extending an eviction ban and rent freeze for those impacted by the Covid-19 pandemic.
"Eamon Ryan has been very clear: TDs and Senators can't be in government and not vote with the Government," the Tanaiste said.
Varadkar's comments are in marked contrast to Taoiseach Micheal Martin, who on Friday said it was up to the Green Party leader to decide how to discipline his TDs.
Minister of State Joe O'Brien and his Green Party colleague Neasa Hourigan were banned from speaking in the Dail for two months for not voting with the Government. However, most of the ban will be served during the six-week Dail recess when the Oireachtas is not sitting.
Ryan said that his parliamentary party agreed "you cannot vote against the Government if you're in government". He added: "You cannot abstain if you're in Government. It weakens our strength. It weakens government. It doesn't work."
Interviewed on RTE on Friday, Hourigan said she would not "make a habit" of voting against the Government but insisted she did not believe the legislation brought before the Dail by Housing Minister Darragh O'Brien offered strong enough protections for renters.
There is concern in Fianna Fail and Fine Gael over securing the votes of Green Party TDs when the Budget is put before the Dail in October.
A senior Fianna Fail source also warned the economic impacts of Covid-19 will "hit really hard" in the autumn and said the Government will have to be "very vigilant".
"The stimulus package will help shield the country from the worst of it and we are focused on a steady, cautious return of the new normal," the source added. Separately, Leo Varadkar has insisted the Government enacted significant legislation during its first month in office.
The Tanaiste highlighted the €5bn July Jobs Stimulus Package, the extension of the pandemic unemployment payment and the temporary wage subsidy scheme.
He also noted the extension of protections for renters impacted by the Covid pandemic and the €2bn loan scheme for business, which the Department of Enterprise drafted.
"It's a pity all that got obscured by the missteps and avoidable errors," he added.
Over the summer break, the three parties are expected to develop new structures and processes to ensure there is better communication between the Coalition partners.
The Government's first month in office has been marred by a series of controversies that overshadowed their work on reopening the country after months of lockdown due to the coronavirus pandemic.
Last week, three ministers of state returned a €16,000 pay increase, following a public outcry, but split two identical pay increases to ensure they each got around €11,000 each. Taoiseach Micheal Martin also announced he was taking 10pc pay cut, but it has emerged he will still be earning more than his predecessor, Leo Varadkar.
TDs drown their sorrows as Coalition founders, pages 4-5
Initially, they thought it was a mistake. TDs sitting socially distanced in the vast theatre of the Convention Centre figured a Coalition deputy had inadvertently voted against the Government. Sure, Fine Gael minister Simon Coveney had done it by accident earlier in the week. No big deal.
At one level, the Government has only itself to blame for its incoherent start. The real problem, however, is not the failure of what is a novel three-party Coalition to hit the ground running; this was to be expected in the first few weeks - particularly during a health and economic crisis. No, the real problem is much more insidious than that.