The 1998 Offences against the State Act and the 2009 Criminal Justice Act have been extended for another 12 months.
The Cabinet approved the now annual extension following a request from Justice Minister Charlie Flanagan.
Mr Flanagan secured Government approval to bring resolutions before the Houses of the Oireachtas agreeing that certain sections of the Offences Against the State (Amendment) Act 1998 and Section 8 of the Criminal Justice (Amendment) Act 2009 should be renewed for a further 12 months from 30 June 2020, a government statement said.
The resolutions are to be moved when both Houses of the Oireachtas are in a position to deal with them.
The legislation requires that the sections in question must be renewed by the Oireachtas at specified intervals.
The relevant sections were continued in force for a period of 12 months beginning on 30 June 2019.
The Offences Against the State Act was enacted in the aftermath of the bombing at Omagh.
It contains a number of important anti-terrorism provisions including the offences of directing an unlawful organisation, training persons in the making and use of firearms and withholding of information.
It provides for, amongst other things, inferences to be drawn from a failure to answer material questions and extensions of the period of detention in certain circumstances.
The Criminal Justice Act 2009 was enacted in July 2009 to tackle organised crime.
Among those measures was section 8, which provides that certain serious organised crime offences are to be tried in the Special Criminal Court unless the DPP directs otherwise. The purpose of the provision is to guard against the intimidation of jurors/potential jurors or jury tampering in particularly serious cases.