The justice minister said large vehicles blocking critical infrastructure would be removed.
Protests over the Irish government's response to rising fuel prices entered a third day on Thursday.
Several distinct but co-ordinated protests began on Tuesday involving slow-moving convoys on motorways and blockades on major roads in Dublin and other cities.
Hauliers and agricultural contractors using large trucks and tractors are among protesters disrupting traffic.
On Wednesday, protests escalated with vehicles blocking fuel depots.
In a statement on Thursday, Justice Minister Jim O'Callaghan said "the blocking of critical national infrastructure will not be permitted to continue and the assistance of the Defence Forces has been requested"
He added owners of the vehicles involved in the blockades "should remove them immediately this morning and should not complain later about any damage caused to those vehicles during removal".
The military confirmed they had received a request for assistance from police and said because "this operation is ongoing" they would not be commenting further.
They have four heavy-lift recovery trucks available to help clear trucks and tractors involved in blockades and it is understood it is envisaged that assistance will be limited to these vehicles and the personnel required to operate them.
The Defence Forces also said images of a convoy of Mowag armoured personnel carriers circulating on social media are "the personnel of the 128th Infantry Battalion conducting mission readiness exercises ahead of deployment to UNIFIL next month".
Irish Prime Minister Micheal Martin told RTE he did not "anticipate" there would be violence if the army and gardai (police) moved in on demonstrators.
Martin said it was "not in our nature to be engineering any situation that gives rise to conflict".
Martin said "the government had to act" once the Whitegate oil refinery in County Cork and the Foynes fuel terminal in County Limerick were blocked.
Defence Minister Helen McEntee told reporters at the Curragh Camp that the Defence Forces intervention was "never a first resort".
In a statement at Garda headquarters in Dublin, Deputy Commissioner Shawna Coxon said gardai were "moving to an enforcement phase" unless protesters "desist and disperse".
She added: "An Garda Siochana is advising protesters to immediately cease blockades of such critical national infrastructure or face the full rigours of the law."
The protesters say they have nominated "three or four" spokespeople they want to meet government leaders.
However, speaking on RTE radio, one of them, John Dallon said he does not speak for the protesters blocking fuel depots: "I'm here on the streets of Dublin, I have no voice as regards what's happening down the country as regards blocking up ports."
He added: "What's happening down there is out of my hands, I have no control over what happens."
Agriculture Minister Martin Heydon said he would meet with farming and haulier representative groups but would not speak to the protesters.
He said: "What is very clear here is that this is a clear choice between democracy or anarchy, and we have a rule of law in this country.
"I completely understand where people's frustration is from in terms of (the) very high energy shock as a result of the war that has broken out between America, Israel and Iran."
Fuels for Ireland chief executive Kevin McPartland said there was a risk to supplies to petrol forecourts as a result of fuel depots being blocked.
Two weeks ago, Ireland's ruling coalition signed off on a range of measures to reduce fuel costs including a temporary excise duty reduction for motor fuels, expansion of the diesel rebate scheme for hauliers and an extension of the fuel allowance.
It resulted in a reduction of 17 cents for petrol, 22 cents for diesel and five cents for green diesel - but the savings were largely eroded as the Iran war raged on.
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