DUP MP Sir Jeffrey Donaldson has accused the Taoiseach of showing "poor manners and disrespect" for visiting Northern Ireland "outside of normal protocol".
A spokesman for Leo Varadkar denied the claim and insisted that "standard protocol" had been followed. The Taoiseach said he wasn't "an invader" and had been trying to be "a good neighbour" with his visit.
Mr Varadkar visited Lurgan and Warrenpoint after meeting EU chief Brexit negotiator Michel Barnier in Dundalk.
Sir Jeffrey said: "Leo Varadkar's visit is another demonstration of the poor manners and disrespect which appears to be the Irish government's Brexit strategy.
"Having told unionists just over a month ago that he recognised statements and actions by the Irish government were unhelpful or intrusive, he follows this up with a visit which no local representative is informed about and none of the other normal protocol is followed."
The DUP MP continued: "It is increasingly apparent that the Irish government does not seem to care about securing a sensible and pragmatic outcome from Brexit which can work for both Northern Ireland and the Republic.
"Their preferred approach is to use Brexit in whatever way possible to undermine Northern Ireland and particularly its constitutional position."
However, a spokesman for Mr Varadkar denied there had been any breach of protocol. He said: "Mr Varadkar is using the visit to meet young people at an integrated school, visit the Jethro Centre in Lurgan and meet with business people in Warrenpoint to speak about the impact of Brexit.
"Visiting Northern Ireland regularly is a priority for the Taoiseach. As is standard protocol, the Northern Ireland Office was informed."
Mr Varadkar told the BBC: "I really just wanted to do something different.
"I can assure anyone that I am not an invader, I just want to be a good neighbour. I received a very warm welcome."
Last week, Brexit Secretary David Davis was criticised for failing to meet local politicians or journalists during a visit to Co Armagh. His department later apologised for breaching protocol by failing to inform the local Sinn Fein MP Mickey Brady about his visit.
Meanwhile, DUP MEP Diane Dodds last night accused Dublin of failing to engage with innocent victims of terrorism in border communities.
She said: "The Taoiseach and Irish Foreign Affairs Minister have been very willing to involve themselves in issues affecting border communities in Northern Ireland, not least in relation to concerns surrounding the UK's exit from the EU.
"The Irish government however is less keen to engage with the families of those murdered by republican terrorists in the same areas - particularly where there is suspicion of state collusion.
"Had Mr Varadkar offered some notice of his most recent visit then questions could have been asked about the lax security policy along the border during the IRA's terrorist campaign.
"This may be one aspect of the border which the Taoiseach is less keen to talk about."
Mrs Dodds accused Dublin of failing to respond to a "dossier of substantive correspondence" sent by the family of Ian Sproule, who was killed by the IRA in Castlederg in 1991.
There have been allegations that gardai passed on information to republicans which was used to justify the 23-year-old's murder.
Mrs Dodds claimed the Irish government's track record "shows scant regard for the needs of innocent victims of terrorism across Northern Ireland".
She added: "If the Taoiseach is genuine about meeting the needs of everyone in border communities, he should address this failure as a matter of urgency."