In earlier visits to London and Dublin, key brokers in the peace process, she said the men of violence were history and vowed US political support for the province's leaders, and US investment for its economy.
During a press conference in Dublin with Irish Prime Minister Brian Cowen, Clinton said remaining differences can be overcome.
"Clearly there are questions and some apprehensions," the chief US diplomat said.
"But I believe that due to the concerted effort of the British government, the Irish government, the support of friends like us in the United States, that the parties understand that this is a step they must take together," she said.
The efforts are aimed at defusing a simmering stand-off between Northern Ireland's leaders over the transfer of police and justice powers from London to Belfast.
First Minister Peter Robinson's pro-British Democratic Unionists (DUP) and his deputy Martin McGuinness's republican Sinn Fein agree in principle on the transfer of responsibility, but disagree over the timing.
The power-sharing administration took office in Belfast in May 2007 after a landmark accord between the Protestant DUP and Catholic Sinn Fein, long fierce rivals.
In addition to the political row, fears of fresh violence have grown since two British soldiers and a policeman were killed in March, in attacks claimed by the Real IRA and another dissident republican paramilitary group, the Continuity IRA.
In a move apparently timed to coincide with Clinton's visit, a republican group responsible for dozens of murders during three decades of violence in Northern Ireland announced it was laying down its arms.
The Irish National Liberation Army (INLA), a splinter group of the Irish Republican Army (IRA) whose most high-profile attack was the 1979 killing of Airey Neave, an aide to Margaret Thatcher, said "the armed struggle is over.
"The objective of a 32-county socialist republic (uniting Ireland) will be best achieved through exclusively peaceful political struggle," said a spokesman for the INLA's political wing, the Irish Republican Socialist Party.
As well as political help on justice and policing, Clinton also pledged US economic help.
She noted that Washington has appointed Declan Kelly as a special economic envoy to show it is serious about maintaining the US support which has flowed since 1993, when she was US first lady.
In London earlier, Clinton stressed the need to fully implement the peace process started by the 1998 Good Friday Agreement, which ended three decades of the so-called Troubles in Northern Ireland which killed at least 3,500 people.
"To me terrorism is terrorism. Those who would try to disrupt the peace of people going about their daily lives are out of step and out of time," she told reporters after talks in London with British Foreign Secretary David Miliband.
Clinton's husband Bill was heavily involved in the Northern Ireland peace process during his time as US president. US envoy George Mitchell helped broker the Good Friday accord, alongside then British and Irish leaders Tony Blair and Bertie Ahern.
During her planned speech Monday in Belfast's Stormont seat of government, Clinton was to say: "I will certainly provide as much encouragement and support as I can" in efforts to resolve the deadlock.
Clinton will be the highest-ranking foreign government official to address the devolved body, according to officials organising the secretary's trip.
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