Taoiseach Bertie Ahern refused to be drawn on a report that there were up to six Islamic terrorist cells operating in Ireland in 2003.
Fine Gael leader Enda Kenny said that when he had raised the matter previously, Mr Ahern had said that some people were being observed.
"Does the evidence available to the Government indicate that these Islamic terrorists cells are still based in Ireland or that personnel associated with them are still based here?" he asked.
"What is the latest information available to the Government and is the Taoiseach happy that if these invididuals are here, their activities are not illegal? Is the Taoiseach satisfed that, if such individuals were involved in planning terrorist activities, the matter has been addressed?"
Mr Ahern said it was not appropriate to speculate but he could assure the House "that the Garda Síochána closely monitors the security situation, including threats to international security, on an ongoing basis".
He added that a small number of people was closely monitored and those under observation changed from time to time. "The situation in this regard has not changed greatly in the past year," he said. Labour leader Pat Rabbitte asked if the threat from terrorist groups was more extensive than people were told, or "is there another explanation for the frequency of resort to examining telephone records by the Garda Síochána, given the revelation some time ago that in 2006 there were 10,000 such requests by the Garda?"
Mr Rabbitte said that seemed to be an extraordinarily high number of such Garda examinations. "Does the Taoiseach agree with the assistant Data Protection Commissioner," he asked, "who concluded that perfectly innocent people are having their private records pored over, or can he give a logical explanation as to why there should be this frequency of resort to examining the private telephone records of citizens?"
Mr Ahern said that the Garda was continually involved in monitoring ongoing subversion by, thankfully, a limited number of groups and, of course, there were criminal groups.
"I do not have a breakdown," he said. "This is a matter for the Department of Justice, but the Garda is monitoring criminal gangs, subversives and a small number of people who are or may be associated with international terrorism all the time."