Secretary of State Hillary Clinton announced Tuesday that Pakistan was reopening ground supply lines into neighboring Afghanistan after she apologized for the death of 24 Pakistani soldiers in a NATO strike in November.

"We are sorry for the losses suffered by the Pakistani military," Clinton told Pakistani Foreign Minister Hina Rabbani Khar by telephone. America's top diplomat said in a statement that she had also offered "our deepest regrets for the tragic incident" on Pakistani soil that led that country to shut the supply lines.

[Related: Read Hillary Clinton's full statement]

American and NATO officials had said that the closure of the routes had not hurt the alliance's war on the Taliban, but that they would be crucial to the plan to withdraw the International Security Assistance Force's (ISAF) 130,000 troops by the end of 2014. Defense Secretary Leon Panetta told Congress earlier this month that the need to rely on other supply lines was costing NATO an additional $100 million per month and suggested perhaps imposing limits on America's aid to its sometimes fitful ally.

"Foreign Minister Khar and I acknowledged the mistakes that resulted in the loss of Pakistani military lives," Clinton said. "We are committed to working closely with Pakistan and Afghanistan to prevent this from ever happening again."

The stalemate over the supply lines was just one of many symptoms of fraying ties in the aftermath of the May 2011 Navy SEAL raid that killed Osama bin Laden at his hideout in a garrison city in Pakistan. Pakistani authorities expressed anger that they had not been consulted. American officials charged that some Pakistani officials must have known that the al-Qaida mastermind was there. Relations have also suffered from escalating American drone strikes inside Pakistan. And American lawmakers had increasingly discussed the possibility of reducing—or tying strings to—military and economic aid from Washington.

"America respects Pakistan's sovereignty and is committed to working together in pursuit of shared objectives on the basis of mutual interests and mutual respect," Clinton said.

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"Our countries should have a relationship that is enduring, strategic and carefully defined, and that enhances the security and prosperity of both our nations and the region," she said.

Clinton said that her Pakistani counterpart "has informed me that the ground supply lines into Afghanistan are opening." Pakistan will not charge a transit fee, she added, calling that "a tangible demonstration of Pakistan's support" for NATO's goals in Afghanistan.

"This will also help the United States and ISAF conduct the planned drawdown at a much lower cost," Clinton said. But "no lethal equipment" will pass through that route except for weapons going to Afghanistan's security forces.

The standoff cast a cloud over NATO's summit in Chicago in May. American officials had privately expressed hope that the stalemate would be broken before the gathering, which Pakistani President Asif Ali Zardari attended. President Barack Obama briefly spoke to Zardari but did not hold a full-fledged bilateral meeting—a move seen in some circles as a snub related to the supply lines issue.

At the summit, NATO Secretary-General Anders Fogh Rasmussen told reporters that the transit routes' closure had not affected the war effort "so far."

"But it goes without saying that it will be quite a logistical challenge to draw down the number of troops in the coming months and years," Rasmussen said. "So we need a number of transit routes, and obviously the transit routes through Pakistan are of great importance, and I would expect a reopening of the transit routes in the very near future."