Leo Varadkar has warned of his unhappiness at the speed of reforms in the scandal-struck Gardaí.
But the Taoiseach voiced confidence in the force's beleaguered chief Noirin O'Sullivan - saying she is fighting many battles on many fronts.
Ms O'Sullivan is again facing calls for her resignation over the latest in a long line of controversies shaking public trust in the Gardaí.
Sinn Féin deputy leader Mary Lou McDonald accused the Garda Commissioner of having "misled" the taxpayer watchdog - the Comptroller and Auditor General (C&AG) - over financial irregularities at the Garda training college.
Ms O'Sullivan wrote to the C&AG on July 31 2015, reassuring him everything was well with Garda finances, Ms McDonald said.
"But the commissioner knew this was not true," she added.
The Garda Commissioner has told a parliamentary committee that she was told about financial concerns at the Garda college on July 27 that year, four days beforehand.
Ms McDonald told the Dail that public confidence in the Garda chief was "in tatters" amid a "virtual conveyor belt of crises that continue to envelop" the force.
Furthermore, the Garda commissioner could not or would not express confidence in her senior management team before the Public Accounts Committee, she said.
"How can anyone have confidence in the head of police, if she cannot express confidence in her own team," the Sinn Féin TD said.
"The Garda Commissioner has to go, her position is absolutely untenable."
But Mr Varadkar said both he and his government have confidence in Ms O'Sullivan.
There are a number of investigations into ongoing controversies - including a Garda Ombudsman probe into suspected fraud at the Garda College and the Charleton Tribunal into an alleged smear campaign against whistleblowers - which needed to run their course, he said.
"The problems that are besetting gardai are long-standing," Mr Varadkar added.
"Many if not all predate (Ms O'Sullivan) becoming Garda Commissioner and I believe that she is someone fighting many battles on many fronts in an effort to put things right."
However the Taoiseach added: "We also need to accelerate the pace of reform in the Gardai. I am not happy with the pace at which reform is occurring in the Gardai."
A bank account in Cabra, north Dublin - not far from Garda headquarters in Phoenix Park - is at the centre of a newly-launched investigation by the Garda Ombudsman in to suspected fraud at the force's training college in Templemore, Co Tipperary.
It was an official Garda account, rather than a personal account, opened in 1999 and closed in 2010.
Ms O'Sullivan has refused to identify the signatories to the account, but said a retired senior officer was one, whose rank would identify the person if disclosed.
The money in the account, in excess of 90,000 euro at times, was from European Union funding.
Olaf, the European anti-fraud agency which investigates fraud against the EU budget, corruption and serious misconduct within European institutions, has been notified about the disclosures.