Kenny, Cameron urge calm as marching season begins
However, Sinn Fein was last night calling on the two governments to intervene to take urgent control of the escalating crisis, which it described as "very bad".
Mr Kenny and Mr Cameron spoke yesterday by telephone to discuss the rising tensions in the North ahead of next Saturday's July 12 celebrations.
The two leaders agreed that Northern leaders have to step up to the plate to ensure calm at this critical juncture.
Last Thursday, the North's parades commission barred a Twelfth of July Orange Order parade from returning along part of the Crumlin Road in north Belfast. As a result, unionist parties pulled out of talks on parades, flags and the past.
But during their discussion, the Taoiseach and the prime minister yesterday recommitted themselves to the existing institutions and called on all sides to engage in dialogue to overcome their current disputes.
It is understood both Mr Kenny and Mr Cameron concluded that the withdrawal from meetings on parades by unionist leaders is not the answer.
The two leaders are now urging party leaders to engage in dialogue in order to minimise the potential for violence in the coming days.
The Northern Executive meeting on Tuesday should discuss the Parades Commission's decision on an Orange parade, Ulster Unionist Minister Danny Kennedy has said.
Saying that he hoped Tuesday's meeting would go ahead, Mr Kennedy said while it should deal with normal business, he hoped it would also deal "with the here and now, the issue of the day – the Ardoyne parade".
On Thursday, First Minister Peter Robinson said the Stormont institutions had been put under threat by the Parades Commission's determination.
However, the deputy first minister, Sinn Fein's Martin McGuinness, said people should abide by the decision and show leadership.
A Sinn Fein spokesman said that the situation is "very bad" and that it was now clear Unionist politicians were being led by the Orange Order.
Yesterday's Drumcree march passed off without incident, but Orange Order District Master Darryl Hewitt called for the 'heads' of the entire Parades Commission, accusing them of creating 'orange and green' areas in Northern Ireland.