Mr Varadkar made the comments after being asked about the Wolfe Tones, an Irish folk band that drew the largest ever crowd to a tent at the Electric Picnic music festival in Stradbally, Co Laois, at the weekend.
The Wolfe Tones have subsequently announced their 60th anniversary concert on October 12 at Dublin’s 3Arena, which has a capacity of 13,000.
The band regularly spark debate over their song Celtic Symphony, which contains the contrversial lline: “Ooh, ahh, up the Ra".
Terror victims have repeatedly condemned the lyrics, which have been given increasing prominence in recent years.
The song has caused controversy repeatedly at the West Belfast Festival and also when a video clip emerged of the Republic of Ireland's women's football team singing the lyrics their changing room earlier this year.
Asked about the popularity of the band, Mr Varadkar said he was at the music festival at the weekend but “didn’t get a chance” to see the Wolfe Tones or the Saw Doctors.
“I probably have a more sanguine view of this than maybe other people,” he told RTE Radio’s News at One.
“People like ballads and they like songs that they can sing along to.
“I think some people maybe read too much into the politics of this.
“But there is one thing that I would say: I believe we are on the path to unification.
“I believe that there will be a united Ireland in my lifetime, and in that united Ireland there is going to be a minority, roughly a million people who are British.
“And you judge the success and the quality of a country by the way it treats its minorities and that’s something we’re going to have to think about.
“Because what is, you know, a Republican ballad – a nice song to sing, easy words to learn for some people – can be deeply offensive to other people.
“Bear in mind in the southern (US) states, for example, when people sing about the confederacy and Robert E Lee, they think it’s an expression of their culture and so on, and that’s what they say.
“But that is deeply offensive to the minority, the black community in America and if we’re going to unite this country and unite the people of this country, a bit like (Co Down comedian and The Late Late Show host) Patrick Kielty says, we just need to have a think about how our words and how the songs we sing might be heard by other people.”
But TUV leader Jim Allister took issue with the Taoiseach's defence of the song.
“It is no surprise that someone who thinks a republican ballad, like ‘Up the Ra’ is just a “nice song to sing” should share the same bloodthirsty goal of an all-Ireland Republic," Mr Allister said.
“It is notable that Varadkar refused to comment on the prospects of an all-Ireland until the Protocol and Windsor Framework was obtained. Now, he boasts of its prospects.
"In my view this is because he recognises the vehicle towards unification that the Protocol provides through its creation of the stepping stone of an all-Ireland economy. All of which is why any thinking unionist should be determined never to accept or operate the Union-dismantling Protocol. Irish unity is the intended outcome of the Protocol and thus it behoves every unionist to thwart it.
“Varadkar might also be emboldened by the defeatist and foolish musings of unelected pontificators who boast of their unionist roots and credentials but play the republican game as useful idiots.”
DUP Deputy Leader Gavin Robinson linked Mr Varadkar’s comments to the opinion polls.
A recent poll by the Sunday Independent/Ireland Thinks found Sinn Fein enjoys the support of 33% of voters in the south while Fine Gael has only 21%.
“Leo Varadkar’s optimism about a united Ireland in the past has had an all too close correlation with opinion poll results in the Republic of Ireland for his party," he said. "Playing up republican credentials hasn’t worked before and its unlikely to work now.
"There have been predictions that a united Ireland is just around the corner virtually since the moment Northern Ireland was established. Support for Northern Ireland within the Union however remains strong and the benefits are clear. Neither Leo Varadkar nor his ill-fated overtures will change that reality."
UUP leader Doug Beattie responded that nationalists should be allowed to promote their own aspirations. “As for me, I lead the Ulster Unionist Party," he said. "I am a unionist, and my aspiration is for Northern Ireland to remain part of the United Kingdom. It is for me and others to make Northern Ireland work as part of the United Kingdom and, in doing so, counter those who advocate for a United Ireland.”
He added: “I do not see a United Ireland in my lifetime. Either way, if you are advocating for a United Ireland, then you need to put a plan on the table. I certainly have not seen one...”.
Mr Varadkar faced some criticism for stating in 2021 that Irish reunification could happen in his lifetime.
In January this year, he declined to answer whether he thought there would be a united Ireland in his lifetime during a panel discussion at the World Economic Forum in Davos.
He said at the time that EU-UK talks on renegotiating the Northern Ireland Protocol – arrangements that outline post-Brexit trade arrangements for the region – had reached a sensitive stage.
Sinn Fein - an opposition part in the Republic - has repeatedly called on the Irish government to set up a Citizens Assembly on Irish unity, which would see 100 citizens discuss issues around how unification would work in practice.