Sinn Fein has accused the DUP of "riding roughshod" over the majority in Northern Ireland who opposed Brexit.
But the DUP hit back that only it has the numbers at Westminster to shape a Brexit deal, while Sinn Finn boycotts Parliament.
The clash came as Brexit continued to dominate the General Election campaign.
Sinn Fein MLA John O'Dowd said: "This election is about Brexit. Theresa May and the Tories want to drag us out of the EU against our will. The DUP have lined up beside the Tory Brexiteers and are attempting to ride roughshod over the democratic will of the people.
"There is no doubt that Brexit is bad for the people of Ireland, north and south. It would be disastrous for our economy, for our agriculture industry, for young people, for the community sector and for those living in border areas.
"The election on June 8 offers people an opportunity to vote against the Tory Brexit agenda and to send a clear message to Theresa May and her DUP allies.
"Sinn Fein is standing against Brexit, against borders, against Tory cuts and for Irish unity."
The DUP's Gavin Robinson said: "This election is an opportunity for people to vote for the Union, and with the DUP they can elect a party with real influence at Westminster to stand up for them.
"Only the DUP can secure the best deal for Northern Ireland as we leave the European Union.
"Whilst the talks at Stormont have been paused, a vote for the DUP is a vote to support the restoration of the Assembly and the Executive."