Details of the two-page letter -- which was delivered to Pakistan's embattled President Asif Ali Zardari late last month -- were leaked to the US media yesterday, hours ahead of Mr Obama's expected announcement of a 34,000-strong troop surge for next-door Afghanistan.
Mr Obama is believed to have offered Pakistan an expanded strategic partnership, including enhanced trade and development aid and help to improve its relations with India.
But he warned the nuclear-armed nation to end the "ambiguity" in its relations with five extremist groups -- al-Qa'ida, Afghan Taliban, the Haqqani network, Tehrik-e-Taliban (Pakistan) and LET -- and work more co-operatively with the US to stamp them out.
The letter was delivered by Mr Obama's national security adviser, General James Jones, during a recent trip to Islamabad, where he told officials that the US military effort to defeat the Afghan insurgency would fail unless Pakistan increased its strikes against those five groups.
A recent review of US policy in the region also acknowledged Pakistan's crucial role, with one senior administration official telling The Washington Post yesterday: "We can't succeed without Pakistan." Another official told the paper: "No matter how many troops you send, if the safe haven in Pakistan isn't cracked, the whole mission is compromised."
Britain is also taking a harder line against the Pakistan establishment's tacit support of groups such as the Afghan Taliban, whose command structure is believed to be openly operate from the Pakistani city of Quetta.
At the weekend, British Prime Minister Gordon Brown said: "People are going to ask why, eight years after 2001, Osama bin Laden has never been near to being caught."