Fianna Fáil Senator Catherine Ardagh called for the setting up of a task force to work on behalf of the undocumented Irish in the United States.
“As with Brexit and most problems, the Government ignores them until such a time as they turn into a crisis,’’ she said.
Ms Ardagh said of the numerous executive orders signed by president Donald Trump, the newest anti-immigration policies scared her most.
"What is most disturbing, and which shows a serious erosion of the rule of law, is the president's sacking of Sally Yates, the US equivalent of our attorney general,'' she added.
Fine Gael Senator Paul Coghlan said people deserved to be protected from conflict and helped to find safety, irrespective of their faith.
“The ban does not target terrorists; it targets vulnerable people and, disproportionately, those of Islamic faith,’’ he added.
Mr Coghlan said president Trump would do well to remember the words of the late, great Monsignor Hugh O’Flaherty who worked so hard to protect and shelter those persecuted during the second World War in Rome.
Monsignor O’Flaherty, he said, had used the phrase “God has no country’’, which was especially relevant at a troubling time across the world.
Independent Senator Lynn Ruane expressed her "disgust and horror'' at the president's executive order.
“If it is discovered that we are colluding on Irish soil in imposing this discriminatory ban, we should no longer offer the service at Irish airports,’’ she added.
Labour Senator Ivana Bacik said the executive order had implications for Ireland.
The US embassy website carried a notice advising anyone who was a citizen, or a dual citizen, of the one of the seven countries not to apply for a visa, she said.
Sinn Féin Senator Rose Conway-Walsh said the ban would undermine efforts to improve relations between peoples of all faiths and nationalities.
“Generations of Irish people fled starvation, poverty and conflict to make a new life and contributed to the building of America,’’ she added.
“Millions of their descendants are among the most outraged at the recent moves.’’