Ahmad Badreddin Hassoun arrived in Dublin on Tuesday as part of a religious delegation from Syria and many of Ireland's Muslims have expressed anger over the decision.
"He's not welcome," said Dr Ali Salim, senior member of the Islamic Cultural Centre of Ireland.
"This man is part of the regime in Syria and we see him as one of the war criminals that should be brought to justice.
"His hand has been stained with the blood of innocents in Syria and he is one of the people who shares responsibility for the killing and displacing of the Syrian people."
Hassoun frequently makes messages of violence during his Friday sermons. In May 2016, he demanded the "extermination" of rebels and civilians living in Aleppo.
"I call upon the Syrian Army to show us its rage and I also call upon our leader to show us their rage in exterminating those criminals," he said.
According to new terrorism legislation, Hassoun could possibly face arrest for his comments under the offence of “public provocation to commit a terrorist offence”.
The Criminal Justice (Terrorist Offences) Act 2014 defines this offence as “a message to the public, with the intention of encouraging, directly or indirectly, the commission of a terrorist activity”.
Irish police refused to comment on the possibility of arresting Hassoun, saying that they do not comment on individual cases.
The Irish Syria Solidarity Movement (ISSM) has also condemned the Mufti's visit and has asked the Irish police to arrest Hassoun for hate crimes.
"This terrorist should clearly not be let into the country, let alone inside the houses of the Oireachtas [the lower house of the Irish parliament] and shame on anyone who was involved in arranging the invitation to him," the ISSM said in an open letter to the Oireachtas.
| The only way to promote peace is through dialogue Dr Umar al-Qadri, IMPIC |
The mufti is visiting Dublin as part of a religious delegation from Syria, lobbying against European sanctions.
The delegation also includes Gregory III Laham, the leader of the Melkite Greek Catholic Church and Ignatius Aphrem II of Antioch, leader of the Syriac Orthodox Church.
The delegation will begin its tour with a visit of honour to the Trinity College Chapel for a "united prayer of peace for Syria", with choristers, senior academics, politicians and senior members of the diplomatic corps also in attendance.
The Muslim Student's Association at Trinity College did not respond to numerous requests to comment.
Shaykh Dr Umar Al-Qadri, CEO of IMPIC told The New Arab that the document affirms the promotion of peaceful coexistence and prohibits the signatory from radicalising other muslims.
"We did not write this document because of him," said Qadri.
"It's a template document used because of muslim speakers that come to Ireland to promote extremism."
Qadri condemned any and all violence in Syria, but argued that he wanted to meet Hassoun in order to help promote a peace process.
"The situation in Syria is very complex and everyone there has handled blood - they are all in my view a part of this crime against humanity," he said.
"But the only way to promote peace is through dialogue."
The delegation will then address the Joint Committee on Foreign Affairs and Trade at the Irish parliament on Thursday at 9am.
Committee Chairman, Brendan Smith TD, said "This meeting is one in a series of meetings held by the Joint Committee in their deliberations on the ongoing atrocities in Syria, atrocities which have been repeatedly condemned in the strongest possible terms by the Joint Committee.
The committee will subsequently receive the novelist Robin Yassin-Kassab to hear his views.
Yassin-Kassab called Hassoun a "genocidal criminal" in a tweet on Wednesday.