Northern Ireland's Democratic Unionist Party said it would withdraw cooperation with Sinn Fein at the top of the region's power-sharing government over the fallout from a banned Protestant parade, but stopped short of collapsing the executive.

The DUP, the region's largest pro-British party, have called for First Minister Michelle O'Neill and other lawmakers from the Irish nationalist Sinn Fein party to be prosecuted for blocking the contentious parade from marching through a Catholic area.

O'Neill and other Sinn Fein lawmakers have been interviewed by police in relation to their investigation into what police have deemed to be an unlawful protest.

DUP leader Gavin Robinson told a news conference on Thursday that all work between O'Neill and his party colleague, Deputy First Minister Emma Little-Pengelly, will cease until the British government sanctions O'Neill for her role in the protest.

He said that while it would be "madness" to collapse the executive with the parties in the middle of budget talks with London, the DUP would keep that option on the table.

O'Neill said the DUP move means she cannot attend a meeting with the British prime minister and first ministers of Scotland and Wales on Friday, calling it a "reactive stunt".

Britain's Northern Ireland minister stepped in earlier this month to overturn a decision by local authorities to grant a permit for the parade after protests triggered a two-week standoff between Catholic residents and Protestant marchers.

The standoff raised political tensions between the two rival parties that share power in a compulsory coalition and has added to the potential difficulty in forming a new power-sharing government after elections to the regional assembly next May.