Mr Kenny said the Church must “measure up to the responsibilities that they accepted”.
Speaking in Philadelphia, Mr Kenny said religious orders must “reflect on the seriousness of this” before they are forced to do so.
He was speaking after Health Minister Simon Harris said there is “significant merit” in looking at seizing hospital and school lands owned by the Church as a means of meeting the €1.6bn cost of sexual abuse redress payments.
Mr Harris said the failure of the Church to meet its commitments is “completely unacceptable” and called on Pope Francis to instruct religious orders here to “pay over and pay up”.
He said the congregations’ current contribution was “pathetic and paltry”, adding that Irish religious leaders should tell them to pay up now.
“What we have to do is look at what we can do and there is significant merit at looking at hospital land and looking at school property,” said Mr Harris. “What I have been thinking about in recent days is what levers are at the disposal of the State.”
He said the State continues to fund hospitals where they are owned by the Church, as well as schools.
“The Government will consider each and every legal tool at our disposal,” said Mr Harris.
He called the 2002 deal between the Fianna Fáil-led government and the Church “economically and socially illiterate”, as it indemnified the Church from the growing cost of redress for abuses.
“There is an outstanding amount under the existing agreement and the current contribution sought from the Church is pathetic and paltry and the fact they haven’t even paid that is going to be pursued immediately,” he continued.
Mr Harris then took direct aim at religious leaders, requesting that “the next time they make a homily and contribute to this public debate, they would call on all religious institutions to pay up and that call should go all the way to the Vatican”.
Mr Kenny said the time has come for the Church to “get on with it” and he “would expect that the Vatican would respond” to issues he previously raised in relation to clerical abuse.
“I would expect that the congregations and the Church would reflect on the seriousness of this and measure up to their requirements,” he said. “I referred a number of matters to the Pope when I met with him last year and I would expect that the Vatican would respond to those.”
To date, religious orders have contributed just 13% to the compensation fund. This contribution is underpinned by an agreement with 18 religious orders negotiated by former Fianna Fáil minister Michael Woods in 2002.
Fianna Fáil TD John McGuinness said he does not believe that agreement was the best one for the State and that it may not be legally watertight.
Archbishop of Dublin Dr Diarmuid Martin said “everything must be done” to enable the truth to emerge. He said the sad facts coming to light around the treatment of children and mothers in Church-run institutions lead us again to challenge the Church in Ireland to a deep self-examination and repentance.
“It is not something that can be wallpapered over or interpreted by clever spin-doctors,” he said.
“Everything must be done to enable the truth to emerge. We must confess the role of the Church in the building-up of a culture which failed to recognise the presence of Jesus in the smallest and the weakest.”