Following talks with his Irish counterpart Enda Kenny, Cameron's office said in a statement that "urgent, intensive and focused cross party talks" would be held.
Cameron and Kenny "agreed that the current situation in Northern Ireland is serious and without urgent progress there is a real threat to the stability of the devolved institutions".
Kenny said the talks should focus on "trust and confidence issues arising from the legacy of paramilitarism".
Gerry Adams, president of Sinn Fein, the republican political party formerly seen as the IRA's political wing but which now shares power with unionists in Belfast, insists that "the IRA is gone and is not coming back".
The situation underlines the fragility of the power-sharing government in Northern Ireland despite a 1998 peace deal which largely brought an end to some 30 years of sectarian civil unrest in which 3,500 people died.
The talks will involve the British and Irish governments as well as Northern Irish politicians.
The Democratic Unionist Party (DUP) of Northern Ireland's First Minister Peter Robinson says Sinn Fein should be excluded from the government and warned it could quit unless the republican party addresses the issue of alleged IRA violence.
The smaller Ulster Unionist Party pulled out of the power-sharing administration last week.
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