LONDON (Reuters) Pakistan is cooperating more with US-backed Afghan peace efforts but not to the extent sought by Washington, the US special envoy for Afghanistan and Pakistan said on Friday. Speaking on a visit to Britain, Richard Holbrooke cited several areas of progress including a greater Pakistani military push against militants on its soil, but an Afghan Taliban faction called the Haqqani network remained a real problem. Without Pakistans participation, this (Afghan) war could go on indefinitely, he said in a briefing for reporters after holding talks with Britains Chief of the Defence Staff, David Richards, and UK National Security Adviser Peter Ricketts. Theres much more cooperation at every level, he said, citing joint efforts to build bilateral military, consular and economic ties and an expanded assault by Pakistani forces against some militants in areas near the Afghan border. But I dont want to mislead you ... it (cooperation) is not yet where we hope it will be, he said. Pakistani action against militants on the frontier is seen as important for bringing stability to Afghanistan, where US forces are leading a major NATO offensive against the Taliban. The Haqqani network, led by Jalaluddin Haqqani and his son, Sirajuddin, is one of three main factions of the Afghan Taliban. The group is blamed for several daring attacks on coalition and Afghan forces and is allied with both Afghan Taliban leader Mullah Mohammad Omar and Osama bin Ladens al-Qaeda. Holbrooke declined to discuss North Waziristan, home of the Haqqanis and other armed groups. Washington has urged Pakistani forces to enter the area to attack fighters there. Everyone talks about North Waziristan but what we talk about is the Haqqani network, he said, citing several attacks inside Afghanistan he said it had launched. Lets be very specific...Its a real problem. Holbrooke reiterated a longstanding dismissal of media speculation about attempts to explore possible reconciliation talks between the Afghan Taliban and US officials. He said the emphasis right now was going on reintegration, a term for efforts to persuade Taliban foot soldiers to lay down their arms and participate in social and development projects. The reintegration policy is the key to a successful counter-insurgency campaign, Holbrooke said. As for reconciliation, its out there somewhere. Weve talked about it. The US will support Afghan-led reconciliation and by that we mean we need to know whats going on. Not much is going on now, and nothing is going on with the United States.