Washington has long been frustrated at Islamabad's reluctance to target the Afghan Taliban's ruling council, the Quetta Shura, which is accused of directing large parts of the insurgency across the border in Afghanistan.
State department and intelligence officials delivered the ultimatum to Asif Ali Zardari, Pakistan's president, last week as he visited the US for the United Nations' security council sessions and the G20 economic summit.
Pakistan's government has argued the Quetta Shura, led by Mullah Mohammad Omar, does not harm Pakistan. It has said that dealing with other militants such as those in the Swat valley was a higher priority.
But last week Anne Patterson, America's ambassador to Islamabad, told the Daily Telegraph that the offensive in Swat was not targeting the insurgents posing the greatest danger to Nato forces in Afghanistan.
An official at the Pakistani interior ministry told the Daily Telegraph: "The Americans said we have been raising this issue with you time and again. These elements are attacking Nato forces in southern Afghanistan, especially in Helmand. The Americans said 'If you don't take action, we will.'"
Rehman Malik, Pakistan's interior minister, said the US had so far been unable to provide detailed intelligence to target the Quetta Shura. He said: "We need real-time intelligence. The Americans have never told us any location."
US unmanned drone strikes have so far been confined to Pakistan's federally administrated tribal border regions where Islamabad holds little sway. But attacks in or around Quetta, in Baluchistan, would strike deep into the Pakistan government's territory and are likely to cause a huge outcry in the country.
Details of the shift in strategy emerged as Barack Obama, the US president, continued to reconsider his strategy for tackling the growing Taliban insurgency in Afghanistan. Gen James L. Jones, Mr Obama's national security adviser, said no deadline had been set for responding to an urgent request for up to 40,000 new troops from the senior Nato commander in Afghanistan.
Gen Stanley McChrystal made the request after delivering a strategic assessment which labelled the situation serious and deteriorating.
Polls show growing US opposition to the war in Afghanistan and several senior democrats have spoken out against sending more troops. Mr Obama said he was a "sceptical audience" to the request.
Joe Biden, US vice president, has argued that Washington should abandon ambitious military proposals and concentrate on more limited operations against al-Qaeda using drones and special forces.
Robert Gates, US defence secretary, denied a rift between the White House and Pentagon over the troop request and said Gen McChrystal was happy for the strategy to be decided before the troop request was considered. Mr Gates rejected calls to set a timetable for withdrawal from Afghanistan and said failure in Afghanistan "would be a huge setback for the United States".
Separately, the Afghan minister for energy and water has survived an assassination attempt when a car bomb exploded, killing at least four civilians and leaving 17 wounded.
The Taliban claimed responsibility for the attack on Ismail Khan, who is one of Afghanistan's key political figures. The bomb exploded in the north western city of Herat as the former warlord's convoy was passing, leaving twisted wreckage littering the tree-lined road.