If border posts return to Northern Ireland they will be attacked, according to the Taoiseach Leo Varadkar.
Mr Varadkar says they will become natural targets for people if they have to be re-established post-Brexit.
But he believes there will not be a return to the violence of the past in Northern Ireland.
Speaking in the US at the start of a week-long St Patrick's Day visit, Leo Varadkar said certain tensions could be re-ignited by a hard border.
"I don't anticipate a return to violence like the kind we had 20 or 30 years ago.
"But if you do have physical infrastructure - if you do have cameras, and signs and border posts - those things will become targets.
"And then what do you do? Do you accept that, or do you then put in a guard to stop them doing that.
"And that's why it might all escalate and go the wrong way".
Taoiseach Leo Varadkar @campaignforleo meeting with @GovAbbott of Texas & First Lady Cecilia Abbott - who has Irish heritage - in Austin this morning #SPD2018 #StPatricksDay pic.twitter.com/qLC2IxV1Zc
— Embassy of Ireland USA (@IrelandEmbUSA) March 11, 2018
Mr Varadkar says he will raise LGBT rights when he meets US Vice President Mike Pence this week.
He says he is disappointed the US is no longer a leader in the gay rights campaign.
Vice President Pence contests the charge that he is in favour of conversion therapy to change someone's sexual orientation.
The Taoiseach says it is an area he intends to discuss with the US leaders.
"What I intend to say is that for the cast majority of people around the world - including people from gay, lesbian and transgender backgrounds - we've always seen America as a beacon of freedom.
"This is the land of the free, the home of the brave: this is where the LGBT rights movement began, the first place where gay people fought back".
Choctaw Nation visit
On Monday, Mr Varadkar visits a Native American tribe that donated money to Ireland during the Great Famine.
The Choctaw Nation in Oklahoma took up a collection of US$170 (€138) for Irish famine relief on March 23rd 1847 - which would be worth thousands today.
This was seen as particularly poignant, given their own history of enduring deprivation.
In 1831, the Choctaw Indians were forcibly removed from their ancestral lands in Mississippi to what is now known as Oklahoma.
A monument to the Choctaw Nation was unveiled in Cork last year. The 'Kindred Spirits' sculpture, by Alex Pentek, stands at a park in Midleton.
A number of gifts will be exchanged, including a Choctaw flute, and speeches will be made by Mr Varadkar and the tribe's chief.
Additional reporting: Jack Quann