Clinton told a hushed, packed chamber in Stormont Parliamentary Building that IRA dissidents were "looking to seize any opportunity to undermine the process and destabilize this government. Now they are watching this assembly for signs of uncertainty or internal disagreement."
"They want to derail your confidence. And though they are small in number, their thuggish tactics and destructive ambitions threaten the security of every family in Northern Ireland," she said. "Moving ahead together with the process will leave them stranded on the wrong side of history."
Almost all of the 108 members of the assembly applauded Clinton's address. But a few backbenchers from the major Protestant-backed party, the Democratic Unionists, folded their arms instead and two senior figures, William McCrea and Gregory Campbell, left the chamber during the ovation.
That reflected Protestant irritation at being told what to do by outsiders, a point that Democratic Unionist officials said they had made earlier in private to Clinton.
First Minister Peter Robinson, who leads both the power-sharing administration and the Democratic Unionist Party, quipped afterward that Clinton should be pleased that everyone at least kept their seat while she was speaking.
"I thought it was a good speech," said Robinson, who did applaud. "Make any speech in the Northern Ireland Assembly and nobody walks out -- it's a bit of triumph."
Clinton conceded this sensitivity in an unscripted addition to her address. "We know what it means to be supportive. And we also know what it means to meddle," she said, emphasizing that the U.S. sought to do the former, not the latter.
But Clinton also told both sides' politicians, in another unscripted addition, that they bore a special responsibility to break down walls of segregation that literally still scar Belfast.
She noted that most residents today live in exclusively Catholic or Protestant districts -- often bounded by walls of brick, barbed wire and steel called "peace lines" -- while their children go overwhelmingly to either Roman Catholic or Protestant-dominated state schools.
"But given time -- and given the leadership that each of you can provide -- the torn fabric of this society will be woven together, stitch by stitch, choice by choice," she said.
Earlier, after 90-minute talks inside nearby Stormont Castle, Clinton stood side by side with Robinson and Deputy First Minister Martin McGuinness -- itself a diplomatic accomplishment, because the rival leaders had not appeared together in seven months.
McGuinness, a former IRA commander and deputy leader of the Sinn Fein party, praised the longtime interest that both Clinton and her husband Bill offered to Northern Ireland.
"I believe that our society is moving forward to a destination of equality and partnership, and you have been with us every step of the way," he told Clinton on the steps of Stormont Castle.
Sinn Fein benefited greatly from the administration of Bill Clinton. He personally overruled British and U.S. State Department opposition to grant Sinn Fein leaders visas in 1994 that encouraged an IRA cease-fire later that year. Sinn Fein was offered a share of power as part of the U.S.-brokered Good Friday peace accord of 1998, a complex pact that sought to leave behind a three-decade conflict that left 3,700 dead.
But Robinson -- whose party boycotted the Good Friday talks but accepted power-sharing with Sinn Fein after the IRA renounced violence and disarmed in 2005 -- is resisting outside pressure for his administration to take responsibility for Northern Ireland's justice system, too.
The governments of Britain, Ireland and the United States believe transferring law-and-order powers from London to Belfast would strengthen the coalition and isolate IRA dissidents scheming in the background to pull the plug on power-sharing.
The dissidents have grown bolder this year, shooting to death two British soldiers and a policeman, the first such killings since 1998.
Robinson insists he has no objection to transferring law-and-order responsibilities from London to Belfast, but Britain first must provide hundreds of millions of extra pounds (dollars) to fund the proposed Justice Department.
Sinn Fein accuses Robinson of using money demands -- at a time of financial crisis and deep British deficits -- as a delaying tactic because he actually opposes Sinn Fein influence in oversight of the justice system. Robinson denies this.
Clinton was concluding the Northern Ireland part of her European tour with visits to Belfast City Hall and nearby Queen's University. She was to travel to Moscow later Monday.