Clinton spoke at a news conference in Belfast with First Minister Peter Robinson, The Daily Telegraph of London reported. She said she had been "distressed" to hear of a death threat against Naomi West, a member of the British Parliament from Belfast.
"There will always be disagreement in democratic societies, but violence is never an acceptable response to those disagreements," she said. "All parties need to confront the remaining challenge of sectarian divisions, peacefully together."
The latest round of violence began Monday with a vote in the Belfast City Council to limit the number of days the British flag flies over City Hall. Loyalist protesters rioted outside the building, attacking police officers, and the fighting spread to East Belfast.
Soon after police discovered an explosive device they said likely was about to be planted by dissidents in Londonderry Thursday, they said they found a letter bomb in a mailbox in Clough, the Belfast Telegraph reported Friday.
Clinton arrived in Dublin Thursday to attend a security conference and then moved on to Belfast. The city is her last stop on a four-day European trip.
She met with Robinson and with Martin McGuinness, the deputy first minister and a leader in the republican Sinn Fein party.
The discovery of the letter bomb at Clough was revealed by police 2 hours before Clinton's arrival. It was found Thursday when officers were alerted to suspicious activity near the mailbox.
Security officials said they believe dissident republicans opposed to the peace process were involved.
Clinton's husband, former U.S. President Bill Clinton, had a key role in the peace process during the 1990s.
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