SEOUL, South Korea - Acknowledging their strained relationship, President Obama and Pakistani Prime Minster Yousaf Raza Gillani vowed today to rebuild the frayed alliance.

"There have been times, I think we should be candid, over the last several months where those relations have had periods of strains," Obama told reporters before the two leaders held private talks on the sidelines of the Nuclear Security Summit. "I welcome the fact that the Parliament of Pakistan is reviewing, after some extensive study, the nature of this relationship."

"I think it's important to get it right. I think it's important for us to have candid dialogue, to work through these issues," he said.

The relationship between the U.S. and Pakistan broke down last May after the killing of Osama bin Laden in a covert U.S. raid on Pakistani soil. The alliance further ruptured in November when a NATO airstrike mistakenly killed 24 Pakistani soldiers.

In retaliation, Pakistan has shutdown the U.S. supply line for its troops in Afghanistan through Pakistan, requiring the U.S. to use a vastly more expensive route. Pakistan's Parliament is currently considering reopening the route.

Both leaders reaffirmed their commitment to working toward a stable Afghanistan, after a series of major setbacks in the country.

"We're both interested in a stable and secure Afghanistan and a stable and secure region," Obama said.

The sentiment was echoed by the prime minister. "We want stability in Afghanistan," he said. "We want to work together, with you, to have peace and prosperity."

Obama also stressed that it's in both the U.S. and Pakistan's interests to see an Afghan-led reconciliation process.