Gardai expect to make arrests in connection with their investigation into a paramilitary display at a republican commemoration in Limerick city.
Inquiries will also be held into a threat to Irish people who serve in the British armed forces that was delivered on behalf of the dissident group, the Continuity IRA.
The threat was made less than a month after the Irish Independent disclosed that local gardai had foiled a plan by the terrorists to murder a British soldier on a visit home to the city for Christmas. The group had also chosen a gunmen for the murder and had sourced the weapon to be used.
It was the second time that a paramilitary display had been organised by dissidents. Last September, masked men fired a volley of shots at the funeral of Real IRA faction leader Alan Ryan in Dublin.
A full investigation into the latest display and the comments made at the annual Sean South commemoration at Mount St Lawrence Cemetery in Limerick has been ordered by Garda Commissioner Martin Callinan.
Irish Justice Minister Alan Shatter said last night that he had been informed by Mr Callinan about the investigation and he did not propose to comment specifically on the incident at this stage.
But he pointed out that he had consistently made it clear that "threats made by and activities of criminal terrorist groups were completely unacceptable and would be met with the full rigours of the law".
The event was organised by Republican Sinn Fein, which is regarded as the political wing of the Continuity IRA, and the threat to British servicemen and women was issued on behalf of Continuity prisoners.
Sinn Fein Limerick city councillor Maurice Quinlivan, who serves on the party's national executive, said he condemned the threats made on Sunday.
"Armed struggle in this country is over and has been over for a long, long time," he said.
"The IRA disbanded in 2005 and these people are running around, pretending they are the IRA. They are not the IRA", Mr Quinlivan added.
"The vast majority of people in this city and country support the peace process and don't support violence. There is no reason for violence and these people should grow up and go away and give everybody a break."
Fianna Fail justice spokes-man Niall Collins also condemned the statement. He described the people who made the threats on Sunday as "plain and simple criminals".
"These people have no political mandate and don't represent anybody -- only themselves. The government has to step up the effort to finally eradicate these people out of our communities," he added.
Republican Sinn Fein spokesman Joe Lynch, who took part in Sunday's march through Limerick, described Mr Collins's remarks as an "intemperate outburst".
"The call from Mr Collins to eradicate republicans is going a bit over the top," he said.