Taoiseach Leo Varadkar has described the killing of Keane Mulready-Woods as "the most gruesome, grotesque murder that I can think of".
He said he intends to visit Drogheda today and vowed that gardai will have the resources to bring the perpetrators to justice.
"I want to reassure the people of Drogheda in particular that we stand right behind them and I'm going to try and get there because I think the whole country is really shocked by this," he said.
"It's probably the most gruesome, grotesque murder that I can think of.
"And to have it perpetrated against a 17-year-old is just particularly beastly.
"We're going to make sure that the gardai have the resources they need both in Coolock and Drogheda to find out who did this and bring them to justice and end this cycle of violence."
Mr Varadkar said a taskforce for Drogheda - like the one to help Dublin's north inner city in the wake of the Hutch/Kinahan feud there - needs to be given consideration.
He said he is confident that gardai will tackle the violence in Drogheda, and that the north inner city shows it is possible to stop it.
"But it does require people getting 100pc behind the gardai," he added, appealing for anyone with information to come forward.
Justice Minister Charlie Flanagan has said he spoke to Garda Commissioner Drew Harris again yesterday to discuss the progress being made in the investigation.
He said he is satisfied that those responsible for the murder of the teenager will be brought to justice.
Speaking on RTE's Today With Sean O'Rourke programme yesterday, Mr Flanagan said: "I'm again appealing to local communities to assist the gardai in order to ensure that the evidence can be assembled to put these people out of business and behind bars."
Mr Flanagan said there are around 370 gardai assigned to Co Louth, with 145 of them stationed in Drogheda.
Labour senator Ged Nash described the Mulready-Woods murder as gruesome, barbaric and medieval, adding that people in Drogheda are "rightly sickened" by what has happened.