Justice Minister Alan Shatter has condemned hate mail sent to mosques and Muslim homes and organisations in the last week.
Copies of the racist and offensive messages were also posted online after first being distributed in the greater Dublin area.
Mr Shatter, who is on a five day trip to Lebanon, Jordan and Israel, warned that incitement to hatred was a criminal offence and raised concerns over the incident with Garda Commissioner Martin Callinan.
"I utterly condemn racism and religious bigotry in all of their forms and am appalled by the nature of these communications," he said.
"Religious intolerance has no place in our society. Incitement to hatred and incitement to violence are offences under our laws."
The Immigrant Council of Ireland called on anyone who receives a threat to report it to the gardai and to inform the organisation.
The hate mail letter, in block capitals, threatened to attack any Muslim man, woman or child at any mosque in Ireland.
It suggested those behind the hate mail were opposed to the building of a new large mosque in north Dublin.
"Muslims have no right to be in Ireland. The Irish people are not happy with your presence in our country which belongs to the true Irish people," it said.
"This land belongs to the Christian faith and we will not allow you to turn it into a Muslim country. Just remember there are more of us and we have more guns than you will ever see. A mosque and Muslims are the devil and a legitimate target and we will attack."
Dr Ali Saleem, a key figure in the Islamic Cultural Centre in Clonskeagh, Dublin, said the community was not worried.
"The letter was written by immature people. It shows ignorance of the reality," he said.
"The person who wrote that failed to understand that most of the Muslims in Ireland, 65,000 of them, are Irish. They are living at home."
He added: "There are 49 mosques in Ireland, nine in Dublin, that again is a highlight that people living in Ireland, regardless of their beliefs and race, they enjoy the freedoms of beliefs and practise. That's very much something that's in harmony with Irish heritage."
Denise Charlton, chief executive, said the hate mail and the threats contained in them were sinister and alarming.
"The language used is that more often associated with right wing extremists which have re-emerged in other parts of Europe," she said.
"The Immigrant Council is committed to working with the Gardai to combat racism and is requesting that the force use all available resources to establish which group or individual is behind the letters and the internet postings and to ensure that they face the full rigour of the law."
Ms Charlton said the response to the hate mail will test the effectiveness of Ireland's incitement to hatred legislation.
She added: "The tone and language of the letter does not allow for ambiguity, it is by any definition an act of hatred and should be prosecuted as such."