(CNN) -- Pakistan has decided to reopen supply routes that the United States and its allies have used for their troops in Afghanistan, U.S. Secretary of State Hillary Clinton said Tuesday.



Clinton also apologized for a friendly-fire incident last November in which coalition forces killed 24 Pakistani Army soldiers at a checkpoint.



Clinton's announcement comes as representatives from the two nations discussed the re-opening of ground supply routes into Afghanistan during meetings this past weekend that included Gen. John Allen, the commander of U.S. and NATO troops in Afghanistan, said a senior U.S. official who wasn't authorized to speak publicly about the sensitive negotiations.



The talks had been stuck on two key issues -- Pakistan's demand to charge more per container shipped across its border, and Pakistan's demand the United States apologize for the friendly-fire incident last November.



U.S.-Pakistan relations plunged to an all-time low when NATO fighter jets attacked a Pakistani checkpoint near the Afghan border, killing the 24 Pakistani soldiers.



The U.S. government expressed regret over the incident but had not issued a direct apology -- until Clinton's statement Tuesday.



"We are sorry for the losses suffered by the Pakistani military. We are committed to working closely with Pakistan and Afghanistan to prevent this from ever happening again," Clinton's statement said. Clinton spoke with Pakistan's foreign minister by phone Tuesday morning, she said.



"The Foreign Minister and I were reminded that our troops -- Pakistani and American -- are in a fight against a common enemy. We are both sorry for losses suffered by both our countries in this fight against terrorists," Clinton said in the statement. "We have enhanced our counter-terrorism cooperation against terrorists that threaten Pakistan and the United States, with the goal of defeating Al-Qaida in the region."



Pakistan, however, agreed not to impose any transit fee with the re-opened routes, Clinton said in a statement.



Pakistan's Foreign Minister Hina Rubbani Khar told Clinton "that the ground supply lines (GLOC) into Afghanistan are opening," Clinton said in the statement.



"Pakistan will continue not to charge any transit fee in the larger interest of peace and security in Afghanistan and the region," Clinton said. "This is a tangible demonstration of Pakistan's support for a secure, peaceful, and prosperous Afghanistan and our shared objectives in the region."



The action will also help the United States and the NATO-led International Security Assistance Force conduct a planned drawdown of troops at a much lower cost, she said. "This is critically important to the men and women who are fighting terrorism and extremism in Afghanistan."



Pakistan closed the supply routes after a NATO airstrike in November killed the 24 Pakistani soldiers near the border with Afghanistan. Clinton said Tuesday she offered her "deepest regrets" to the Pakistani foreign minister for the "tragic incident" in a phone call Tuesday morning.



NATO insisted the airstrike was an accident. President Barack Obama previously had offered condolences but stopped short of apologizing.



Gen. John Allen, commander of U.S. and NATO forces in Afghanistan, welcomes the decision to reopen the supply lines "as a demonstration of Pakistan's desire to help secure a brighter future for both Afghanistan and the region at large," the NATO-led force said in a statement.



Per current practice, no lethal equipment will move into Afghanistan on the supply routes, except for equipment for the Afghan National Security Forces, Clinton said Tuesday.



A senior U.S. official had said Monday the United States and Pakistan were "moving closer" to an agreement on the supply routes.



Allen has traveled to Pakistan several times in recent weeks to meet with Gen. Ashfaq Parvez Kayani, Pakistan's chief of army staff, the NATO-led force said Tuesday, and continue building "the increasingly important and positive military-to-military relationship between Pakistan and ISAF."



A Pakistani official said the country's Defense Committee of Cabinet, a group of top civilian and military leadership, will meet in the next few days to finalize the deal.



On Monday, the senior U.S. official told CNN that the Pakistani transit payment issue "had been successfully negotiated to a resolution, for all intents and purposes."



There had also been "some movement on our (the U.S.) side to possibly go beyond some of the previous statements" regarding the shooting, the official said, as well as some "flexibility from our Pakistani partners."



CNN's Chris Lawrence and Michael Martinez contributed to this report.