Aontú has decided not to bring forward a motion of no confidence in the Government next week and will instead use Dáil time to push for reforms of the Presidential Election nomination process.
On Tuesday, the party announced it would table a motion of no confidence in Tánaiste Simon Harris over what it described as a "crisis" in Children's Health Ireland (CHI) and in the wake of the death of nine-year-old Harvey Morrison.
Harvey, who had spina bifida and scoliosis, died in July and was subject to delays in accessing urgent scoliosis surgery.
However, in response, the Government tabled a confidence motion in Mr Harris, which was passed by the Dáil on Wednesday after 94 TDs voted in favour and 65 against.
Speaking on RTÉ's Morning Ireland ahead of that motion, Aontú leader Peadar Tóibín accused Mr Harris of failing to deliver on a promise he made, as minister for health, that children would not wait longer than four months for a scoliosis operation.
Mr Tóibín added that his party would instead consider bringing a motion of no confidence in the Government next week.
However, the party decided this morning that it would not bring the motion forward, saying it already believed it had succeeded in bringing "as much pressure as possible on the Government to do the right thing for children with scoliosis".
The party added: "If we brought a motion of no confidence against the Government next week, we would not be able to table another such motion for another six months.
"This would rob us of a key tool to pressure the Government at a key juncture in the future. Motions of no confidence should be used sparingly.
"They should be timed to have maximum effect to achieve objectives. Running two, one week after another, would not achieve that objective."
Mr Harris had told the Dáil that he had never claimed to be infallible and that he did not get everything right but always acted in good faith.
He said he was very conscious of the death of Harvey and he had expressed this to his parents.
The Government is working with advocacy groups to agree on the structure of the inquiry into spina bifida and scoliosis services at CHI.
Minister for Health Jennifer Carroll MacNeill has met affected families, and a follow up meeting is being arranged to discuss options.
Aontú said it would instead bring forward a motion focused on reforms to the Presidential Election nomination process, as well as extending voting rights to Irish citizens in Northern Ireland in presidential elections.
Additional reporting PA
