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The election campaign was marred by Taliban threats. Election-day violence on Saturday claimed at least two dozen lives in the port city of Karachi, in the northwest and in the southwestern province of Baluchistan.

Pakistani voters were undeterred. The election commission reported an unusually high 60 percent voter turnout.

Mr. Obama said the Pakistani people had, by “persevering despite intimidation by violent extremists … affirmed a commitment to democratic rule that will be critical to achieving peace and prosperity for all Pakistanis for years to come.”

The new government will be faced with big challenges, including an energy crisis, runaway inflation and the growing Taliban insurgency.

Afghan President Hamid Karzai said he hopes a new government in Islamabad “cooperates in fighting terrorism and sincerely rooting out terrorist sanctuaries.”

Indian Prime Minister Manmohan Singh invited Mr. Sharif to visit Pakistan’s South Asian rival.

India and Pakistan came to the brink of an all-out war when Mr. Sharif was prime minister in 1999. President Bill Clinton had to personally intervene to cool tensions between the nuclear-armed neighbors.

“The U.S. has worked productively with [Mr. Sharif],” said Mr. Riedel, who was present at a tense Blair House meeting in Washington between Mr. Clinton and Mr. Sharif on July 4, 1999, to defuse tensions with India.

Three months later, Mr. Sharif was ousted in a coup by his army chief, Pervez Musharraf, and sent into exile in Saudi Arabia.

“On foreign policy, the big winner is Saudi Arabia and [Saudi] King Abdullah,” said Mr. Riedel. “[Saudi Arabia’s] voice will be heard in Islamabad more than ever.”

Mr. Sharif’s relationship with the army, which closely controls Pakistan’s relationship with the United States, will be significant.

“The central challenge for Nawaz is to control the army and ISI,” said Mr. Riedel, referring to Pakistan’s Inter-Services Intelligence agency. “He must help pick an [army chief] that will work with the civilians.”

Pakistan’s Army Chief, Gen. Ashfaq Parvez Kayani, is slated to leave office in November.

“When you talk about U.S.-Pakistan relationship, these are issues that ultimately come within the purview of the military,” said Michael Kugelman, senior South Asia associate at the Wilson Center.

“Certainly I think a Prime Minister Sharif may push back more on Washington a bit more so than the PPP government has on issues like drone strikes and issues pertinent to the Afghanistan endgame, but ultimately this is the military’s house and the military will be making the decisions.”