Before stops in Ireland and Northern Ireland, Clinton pledged continued U.S. support for the Northern Irish peace process and said those who continued to exacerbate tension and violence "are out of step and out of time."
With her British counterpart, Clinton said there was nothing to suggest that Pakistan's nuclear weapons could fall into terrorist hands despite Saturday's audacious Taliban attack on the army headquarters in Rawalpindi that highlighted security weaknesses.
Clinton said extremists were "increasingly threatening the authority of the state, but we see no evidence that they are going to take over the state. We have confidence in the Pakistani government and military's control over nuclear weapons."
Miliband told reporters at a joint news conference with Clinton that although Pakistan faced a "mortal threat" from extremists, there was no danger of its nuclear weapons being compromised.
He scolded those who might raise the suggestion. "I think it's very important that alarmist talk is not allowed to gather pace," he said.
The Taliban have launched a series of increasingly bold attacks on military and political targets in Pakistan in recent months. The latest came Saturday, when militants dressed in military fatigues attacked the army headquarters, taking dozens of hostages. The 22-hour siege ended Sunday when commandos stormed the building. At least 19 people died in the standoff, including three captives and eight of the militants.
Miliband said he and Clinton had spent much of their time discussing the conflict in Afghanistan, the situation in neighboring Pakistan and the crisis over Iran's nuclear program.
They deferred comment on the Obama administration's review of how to handle Afghanistan, particularly following allegations of fraud in the presidential election in August. But they were firm on Iran, which is defying international demands to come clean about its nuclear ambitions.
Clinton warned Iran that the world "will not wait indefinitely" for proof it is not trying to develop atomic weapons. Iran insists it has the right to a full domestic enrichment program that it maintains is only for peaceful purposes such as energy production.
She said a recent meeting in Geneva in which Iran and six world powers resumed nuclear talks was "a constructive beginning, but it must be followed by action." Miliband added that Iran "will never have a better opportunity to establish normal relations with the international community."
Before leaving London, Clinton met British Prime Minister Gordon Brown at Chequers, the prime minister's country retreat outside London, and stressed that the trans-Atlantic "special relationship" remained strong.
On arriving in Dublin for a brief stop before heading for Belfast, Northern Ireland, Clinton met Irish Prime Minister Brian Cowen and urged communities in Ireland and Northern Ireland to follow through on the peace process.
There's a deadlock between Northern Ireland's rival Catholic and Protestant leaders over transferring responsibility for Northern Ireland's justice system from British to local hands.
"The step of devolution for policing and justice is an absolutely essential milestone," Clinton said. "Clearly there are questions and some apprehension, but I believe that ... the parties understand that this is a step they must take together."
On her way out of Dublin, Clinton stopped at Bewley's cafe for a coffee to go, drawing large crowds on Grafton Street, and took a few sips before ordering a half pint of Harp lager at McDaids, a nearby pub. She was accompanied by the U.S. ambassador to Ireland, Daniel Rooney.
Late Sunday night, Clinton arrived in Belfast, where she planned to meet Monday with Northern Ireland's First Minister Peter Robinson and Deputy First Minister Martin McGuinness. She also planned to address the Northern Ireland assembly and said she would provide lawmakers with "as much encouragement and support as I can."
Cowen said he believed progress on the matter would be achieved "in the coming days."
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