John Major sought to reassure their anxieties at an hour-long meeting in Downing Street with James Molyneaux, the leader of the official Ulster Unionists.
Ministers said the recent spate of shootings by the Ulster Volunteer Force - including the raking with gunfire of a pub at the weekend - were carried out by 'wild men'.
But senior ministers are taking seriously the threat of growing disillusionment of the middle-class Ulster population. They believe the reluctance of the Irish government to agree to abandon its constitutional claim over the North will heighten the Unionist anxiety.
The meeting with Mr Molyneaux will be used by British ministers as a lever on the Irish government to make more concessions over the production of a framework document on the future of Northern Ireland, which has been delayed until the autumn.
Some British ministers believe progress on the framework document by Dublin would have exerted more pressure on Sinn Fein before its conference this weekend, when it is expected to respond to the Downing Street declaration.Reuse content