Arlene Foster has challenged the European Union to ditch the backstop.
The DUP leader also ruled out speculation of a hard border in Ireland if the backstop option is dropped as “spinning tales”.
She made the comments on Friday in a speech to party members in Kesh, Co Fermanagh – a short distance from the border with the Republic of Ireland.
Mrs Foster described the week’s events at Parliament, where MPs voted for an “alternative arrangement” to replace the backstop as “good progress”.
“It was a massive step forward for the party to see a majority in Parliament also calling for such changes,” she said.
“A clear message was sent to Brussels that the backstop is the problem.”
It remains unclear whether the EU will reopen negotiations on the withdrawal deal, with the Irish Government’s Europe Minister, Helen McEntee, earlier saying that Dublin would “absolutely not” accept that.
Mrs Foster conceded that the EU are “tough negotiators”.
“I don’t expect them to roll over within hours,” she said.
“But they must face up to reality. The blockage to getting a deal is the backstop therefore there must be sensible engagement and a pragmatic approach.
“Here in Kesh, we are within walking distance of the border. Local people travel to and fro across the border multiple times every day. It is quite disgraceful for some in Brussels to exploit genuine fears by spinning tales of border posts, troops and queues.
“No one is building border checkpoints. No one is sending troops to the border either.
“Such talk is foolish and careless.”
Mrs Foster also reiterated her party’s position that any form of division between Northern Ireland and the rest of the UK is “unacceptable”.
“If the UK leaves without an agreement in place and the European Union and Ireland are on one side and the UK is on the other, we will all have to work intensively together to ensure that we deliver on our shared goal of avoiding the return of a hard border,” she said.
“We are absolutely committed to doing that, even in those difficult circumstances.”
“A new border east-west is unacceptable to unionists.
“Let’s focus on getting a sensible deal which works for Brussels, Dublin and London.”