Boris Johnson has said it is up to the EU to ensure there is a no-deal Brexit.
The British Prime Minister said that the Withdrawal Agreement has been rejected by parliament three times and the backstop has to go.
He said if the EU cannot compromise, then the UK will crash out on October 31 this year.
Earlier Mr Johnson spoke to the Taoiseach for the first time since being appointed, and they differed on the issue of the backstop, however, he gave Varadkar his commitment.
The UK under no circumstances will have checks at the border in Northern Ireland and we will throw all our energies into sorting out the problems of frictionless trade at the border.
"We can do it, we have all the sorts of technological solutions that are necessary to do it but let's solve those issues in the context of the free trade agreement that we're going to do after we come out."
Taoiseach Leo Varadkar and new British prime minister Boris Johnson have finally spoken by phone this afternoon after a week of radio silence.
A spokesperson for the Taoiseach said he told Mr Johnson he "looked forward to having a long and close working relationship".
Mr Varadkar emphasised to the British PM that "the backstop was necessary as a consequence of decisions taken in the UK and by the UK Government".
He said the EU was "united in its view that the Withdrawal Agreement could not be reopened".
While alternative arrangements could replace the backstop in the future, "thus far satisfactory options have yet to be identified and demonstrated". the Taoiseach said.
Both governments need to be fully committed to the Good Friday Agreement, he said.
Downing Street confirmed Mr Johnson phoned Mr Varadkar shortly before midday on Tuesday, exactly seven days after he replaced Theresa May as the leader of the Conservatives party.
Under long-held diplomatic protocols, it is the responsibility of an incoming leader of a country to phone their counterparts in other nations for an initial phone call.
However, in a move seen as a clear message to Ireland, despite the Taoiseach sending a public message of congratulations a week ago on his appointment, Mr Johnson had pointedly failed to speak with Mr Varadkar throughout his first week in office.
The new British prime minister has in recent days spoken with outgoing European Commission president Jean Claude Juncker, German chancellor Angela Merkel and French president Emmanuel Macron.
In addition, he visited Scottish first minister Nicola Sturgeon in Edinburgh on Monday, has travelled to Wales today and will meet with DUP leader Arlene Foster in Belfast later this week.
However, a meeting with Mr Varadkar has yet to be organised - with the lack of even a phone call causing further damage to the already Brexit-hit Anglo-Irish relations.
The failure for the two leaders to speak until now has led to growing friction between Ireland and Britain. In addition, it has led to mounting Irish political concerns of a growing risk of a no deal crash out Brexit, despite senior Government officials insisting the lack of a phone call has been overplayed.
Downing Street confirmed this afternoon that Mr Johnson spoke to Mr Varadkar about the Brexit crisis, Northern Ireland and other matters.