Irish PM Bertie Ahern steered the EU through the treaty negotiations
"We've made a decision based on the commitment that we gave when we put the constitution together in draft form," Foreign Minister Dermot Ahern said.
He told BBC Radio 4's Today programme, the treaty could be modified in the light of the French and Dutch votes.
Ireland's main parties back the treaty, but no referendum date has been set.
UK Foreign Secretary Jack Straw said on Monday that the EU as a whole would have to decide the future of the constitution.
He told the UK Parliament there was "no point" in pursuing plans for a UK referendum after France and the Netherlands had voted "No".
Crucial summit
French President Jacques Chirac and Germany's Chancellor Gerhard Schroeder say they want the ratification process to continue.
EU heads of government will try to find some way out of the crisis when they gather in Brussels on 16 June for a summit.
Poland and Portugal say they will stick to their plans to hold referendums on the constitution.
The constitution has to be ratified by all 25 member states to enter into force.
Several countries have already ratified it, but so far only Spain did so through a referendum.
In 2001 the Irish people unexpectedly rejected the Nice Treaty. But the following year, they were asked to vote again and they approved the treaty, after reassurances were given over Irish military neutrality.
Despite the strong 'no' votes in both France and the Netherlands, the Irish foreign minister Dermot Ahern has confirmed that Ireland will still hold a referendum on the proposed European Union constitution. This comes following the Irish rejection of the Nice Treaty in 2002.

Speaking to BBC radio Mr. Ahern said "We've made a decision based on the commitment that we gave when we put the constitution together in draft form." He went on to say "Over 50 percent of the population of Europe have already ratified the convention. What do you say to those people: 'Your votes mean nothing'?" (note that the only country where the constitution was directly ratified by the population and not by the parliament so far is Spain). Unlike in most European countries, in Ireland by law any change to the core treaties of the EU must be put to a referendum.

The constitution was agreed upon by EU heads of state earlier this year under Ireland's European presidency. It is backed by all major Irish political parties including the main opposition, Fine Gael.