Simon Harris hopes laws will be in place for next year
It is understood legislation to allow abortions here will not be introduced into the Dáil until the autumn.
The Government has received legal advice that it cannot proceed to make new laws until court challenges to the referendum result have been decided.
Health Minister Simon Harris says he is still confident the new laws will be in place for the start of next year.
But he has warned there has been a delay to the process.
"My understanding, based on legal advice, is that as of today the Eighth Amendment remains in the Constitution until the president finds himself in a position to sign the referendum bill - and obviously that requires the legal process to be concluded.
"So whilst the people of Ireland have very clearly voted to repeal the Eighth Amendment just under three weeks ago, and I very welcome that decision, and it does herald a new opportunity to care for women here in our own country - that can only take effect in terms of removing the Eighth from the Constitution when the legal challenges are finished".
"My understanding is that the High Court is due to hear the issue on the 26th of June, so obviously it would be inappropriate for me to comment further than that cause the court can order its own business and obviously the court will make its own decisions.
"I am obviously conscious, though, that people do have the right of appeal generally to other courts as well.
"So I think it is likely that you're looking at an early autumn introduction of the legislation".