Foster said her party, which has 10 lawmakers in the UK parliament, was not bluffing in its tough stance on the talks.
"This is no game. Anyone engaging in this in a light-hearted way foolishly fails to grasp the gravity of the decisions we will make in the coming weeks," Foster said.
"The coming days, weeks and months will be critical. The decisions taken will shape the type of Northern Ireland that our grandchildren will live in."
Foster said she wanted to secure a deal that would work for both Northern Ireland and the Republic of Ireland and said she would travel to Dublin for talks on Monday.
In an article in another Northern Ireland newspaper, the Belfast News Letter, former British foreign minister Boris Johnson also took aim at the backstop, describing May's agreement to accept a backstop as a "dreadful mistake".
"The only way to put things back on the right track is to ditch the backstop...," Johnson wrote.
