The Taoiseach, Mr Ahern, has urged a measured response to the terrorist atrocities.
The response, he said yesterday, had to be an international one and kept within the terms of United Nations anti-terrorism conventions. He said it was unlikely there would be any Irish military involvement and he hoped that "a whole lot of countries" would not be drawn in.
It was most important in the days ahead, said the Taoiseach, that it be kept as an "international issue" and not just an American one.
Asked if the Irish Government's offer of support for the US was unconditional, Mr Ahern said: "No, I think that's the point," adding that it had to be kept within the United Nations Convention 1269 (a 1999 Resolution), "which are the rules that governs this".
The international community, he said, wanted to redouble its efforts to prevent and suppress terrorism, and that included increased co-operation.
Mr Ahern said he appreciated that it was difficult for the US, and that people involved in making decisions on what to do next were under pressure.
"It is an international attack against all the free people of the world, against people who believe in human rights and liberty. I think the more the international connection can be maintained on this, to try to deal with it, the better the response will be."
A number of people had said on Tuesday that the US would respond immediately to the attacks, but it had not, said Mr Ahern.
"They are still working to find out how they can deal with this. They will feel it is being put up to them, that these people have gone a step too far."
The United Nations Security Council had been very clear last week in calling all states to work together, he said. "I hope that the charter of the United Nations will be followed over the next number of days."
Mr Ahern said he accepted the right of the US to have some kind of military response.
"Under the UN charter, self-defence is a right . . . But I think the concern of people will be that a whole lot of countries are not drawn into this, the focus is clearly on Afghanistan," he said on RT╔ radio's This Week programme yesterday.
Mr Ahern agreed it was a concern of people that many more innocent lives would be lost. Afghanistan, he said, was a poor country.
"Many of their people, it's estimated 5 or 6 million people, are in famine conditions. It is an easy thing to bomb territories where people are in famine, but that will not do much to crush international terrorism."
People would be happier, he said, if Osama bin Laden's training camps were the places which were hit.
"A few bombers and fighters going out to take out the ordinary people are not going to resolve that . . . We have realised in this country that trying to beat terrorism is not that simple an issue."
Mr Ahern, when asked if there would be any Irish military involvement said he did "not think that would arise".
"It is unlikely that would arise. Of course while NATO have shown their solidarity during the week, we are not any part of that. We have a role to play in the United Nations and in the UN Security Council, and we all have a role to play in the suppression of international terrorism."
On Saturday, Mr Ahern was interviewed on CNN and he said that Ireland was a militarily neutral country "but we have always played an honourable and a very significant position in the UN and we will continue to do that. Ireland has always stood with the US. Ireland has had a special relationship with the US. America has always been very helpful to Ireland."
He said Ireland would be taking over the presidency of the UN Security Council on October 1st for a two year term.
The Labour Party leader, Mr Ruair∅ Quinn, said politics was the real alternative to terrorism. What was witnessed last week in New York and Washington was an act of war, he said yesterday.
Our response would define us, he said. Restraint and patience were not signs of weakness but of strength. It was imperative that those responsible be brought to justice, but it was also critical that they not be afforded victory.
"Victory for them would be a worsening of relations between the western world and the Muslim world. Theirs is the goal of a new cold war that sets the Christian world and the Muslim world at odds in this new century," he said.