The American commanders spoke with Holbrooke this weekend, The New York Times reported.
Over the past two days, Holbrooke visited all four regional command centers in Afghanistan, and the message from all four followed similar lines: While the additional American troops, along with smaller increases from other NATO members, have had some benefit in the south, the numbers remain below what commanders need.
The total number of American soldiers and Marines in Afghanistan is now about 57,000. It was unclear whether the commanders told Holbrooke exactly how many additional troops might be required.
Eastern Afghanistan, in particular, has been a trouble spot. On Sunday, during Holbrooke's stop at the Bagram military base, Major General Curtis Scaparrotti, commander of the United States and NATO forces in eastern Afghanistan, told him and visiting mediapersons that the Haqqani network was expanding its reach.
"We've seen that expansion, and that's part of what we're fighting," The NYT quoted him, as saying.
American commanders believe that the network, whose leaders Jalaluddin Haqqani and his son Sirajuddin have been linked to Al Qaeda, are using sanctuaries in Pakistan to launch attacks against American and Afghan forces.
The problems in Afghanistan have been aggravated by what the American commanders call the Pakistani military's limited response to the threat of militants based there.
Although General Scaparrotti said that cooperation by Pakistan and the United States against the militants had improved recently, he stressed that it was important for the Pakistanis to keep up the pressure, particularly after the reported killing of Baitullah Mehsud.
Holbrooke visited regional command centers in Kandahar, Herat, Mazar-i-Sharif and Bagram on Saturday and Sunday.
Speaking to Afghan reporters at the NATO base in Mazar-i-Sharif, Holbrooke said that part of the new strategy would include reaching out to members of the Taliban who show a willingness to lay down their arms.
