Alternative arrangements to inspections on the border in Ireland cannot be a replacement for the backstop, the Taoiseach has told reporters in Brussels.
Leo Varadkar said that there was no evidence that such alternative arrangements would be effective and that such evidence was unlikely to be seen before the Brexit deadline at the end of October.
Mr Varadkar said that the European Council had reaffirmed last night that the Brexit Withdrawal Agreement could not be reopened for negotiation and that the backstop cannot be removed from it.
He said Ireland would be obliged to protect the Single Market in the event of a no-deal Brexit.
However, he said he saw regulatory alignment as the only way to avoid a hard border. Discussions are ongoing between the European Commission and Ireland on this, he said.
The Taoiseach said that the European Council had also reaffirmed that there could be no bilateral or intergovernmental negotiations on Brexit between the UK and individual EU states.
Asked about the filling of the top jobs in Europe, Mr Varadkar said it was important to have "good people whose perspective is in line with Irish thinking" on Brexit.
Also asked if he would support a future bid by Michel Barnier to be European Commission President, the Taoiseach said that Manfred Weber remained the European People's Party candidate, but that this would be discussed at the group's meeting before the 30 June EU Council summit.
Meanwhile, Brexit will become more "exciting" than before with a change of British prime minister, European Council President Donald Tusk has said.
He told a press conference at the end of the European Council summit: "Now we are waiting for the new British prime minister and we have to be very precise and also patient.
"It's waiting for the decisions or maybe new proposals, but our position remains as I informed just five minutes ago.
"Maybe the process of Brexit will be even more exciting than before because of some personnel decisions in London, but nothing has changed when it comes to our position."
Mr Tusk said the leaders of the remaining 27 member states had agreed on a united approach to Brexit, saying: "We look forward to working together with the next UK prime minister.
"We want to avoid a disorderly Brexit and establish a future relationship that is as close as possible with the UK.
"We are open for talks when it comes to the declaration on the future UK-EU relations if the position of the United Kingdom were to evolve - but the Withdrawal Agreement is not open for renegotiation."
European Commission president Jean-Claude Juncker told the press conference: "We repeated unanimously that there will be no renegotiation of the Withdrawal Agreement."