The New IRA's alleged leadership were secretly recorded in talks about a "hard economic bombing campaign" and cyber attacks on the United Kingdom, the High Court heard on Monday.
The possibility of targeting Shannon Airport in the Republic of Ireland because of its use by American troops was also discussed, it was claimed.
Details emerged as bail was refused to a grandmother accused of being a high-ranking and dedicated terrorist.
Ruling that 49-year-old Amanda McCabe must remain in custody, Mr Justice McAlinden said: "This is absolutely mad stuff being discussed in these meetings."
McCabe, of Ailsbury Gardens in Lurgan, Co Armagh, is charged with belonging to a proscribed organisation and two counts of preparation of terrorist acts.
She is among 10 people facing prosecution as part of Operation Arbacia, a major police and MI5 investigation into the New IRA's activities.
The surveillance-led probe involved bugging two suspected meetings in Co Tyrone earlier this year.
Audio and video recordings were taken from alleged gatherings at properties in Sixmilecross and Omagh in February and July.
Opposing McCabe's application for bail, a Crown lawyer claimed she was one of the high-ranking IRA members present on both occasions.
"She is and was a dedicated terrorist over a period longer than simply the period covered by the two meetings, and she was an advocate of violence and violent attacks," he said.
"In one particular passage (of the alleged recordings) she despaired at the ceasefire called by the IRA on a previous occasion."
It was contended that McCabe poses a risk to the public and national security.
"This applicant is part of the leadership of the IRA who discussed, amongst other things, a hard economic bombing campaign, and inquired about the prospect of carrying out cyber attacks within the UK," prosecution counsel added.
Defence barrister Joseph O'Keefe insisted his client has a clear record and must be presumed innocent.
But Mr Justice McAlinden held there was prima facie evidence of a woman allegedly prepared to go to "extreme lengths to cause either serious damage to the British state or death or serious injuries to perceived agents of the British state in furtherance of her political ideals".
Referring to the alleged recordings of McCabe, he said: "This lady can be linked to making pretty horrendous assertions in terms of what she would like to see happen to various people by the use of torture.
"Even, the prosecution say, some sort of bombing attack on Shannon Airport to show support for Arab terrorist because of the use of Shannon Airport for the transportation of American troops."
Denying bail, the judge identified "clear and unmanageable risks" McCabe would either re-offend, flee or interfere with the course of justice.