Washington (CNN) -- The Taliban is weakened, but the ability of insurgents to hide across the border in Pakistan is the greatest threat to success in Afghanistan, according to the latest Pentagon evaluation of the war, released this week.
"The insurgency's safe havens in Pakistan, as well as the limited capacity of the Afghan government, remain the biggest risks to the process of turning security gains into a durable, stable Afghanistan," according to the "Report on Progress Towards Security and Stability in Afghanistan," a congressionally mandated evaluation of the war's progress that is provided twice a year.
The report comes at a time when American support for the 10-year war is at an all-time low. According to a CNN/ORC International Poll released Friday, only 34% of the public say they support the war in Afghanistan, one point less than the previous low of 35%, with 63% opposed to the conflict.
The report points directly at Pakistani authorities for aiding the strength of insurgents on that side of the border.
"Pakistan's selective counterinsurgency operations, passive acceptance -- and in some case, provision -- of insurgent safe havens, and unwillingness to interdict materiel such as IED components, continue to undermine security in Afghanistan and threaten ISAF's (International Security Assistance Force) campaign," the report says.
On Thursday, the deputy U.S. military commander in Afghanistan raised one example of how the Pakistani military is complicit in insurgent attacks.
"We have seen indications where fires have originated from positions that were in close proximity to some Pakistan outposts," Lt. Gen. Curtis Scaparrotti told Pentagon reporters. "You'll see what just appears to us to be a collaboration or was a collaboration or, at a minimum, looking the other way when insurgents conducted rocket or mortar fire in what we believe to be visual sight of their posts."
The report looks back over the six-month period ending September 30 and was delivered to Congress on Thursday afternoon. Eight of these so-called 1230 reports -- known for the part of the legislation which requires regular assessment of security and stability -- have been issued.
At a Friday afternoon briefing at the Pentagon, officials from the Defense Department and State Department emphasized that the report showed progress, as well as a focus on challenges ahead.
"We are succeeding, the president's strategy is succeeding, the sacrifices of the American troops in Afghanistan are being rewarded, the efforts are being rewarded with success," said a senior defense official, who can't be identified by name under the ground rules of the briefing.
In response to a question about falling public support (the poll) officials pointed to what they said were "widespread misperceptions" about the war, with a too-frequent focus on high-profile attacks while ignoring behind-the-scenes success such as improvement in the Afghanistan security forces.
"We want people to be able to draw their own conclusions from the report," the senior defense official said. "Certainly my personal message is that we are having much more success than people realize."
The latest assessment cites sustained progress and improvement in security, as well as advances by local forces in seven parts of the country, including the capital, covering 25% of the population.
But by a variety of measurements -- including overall violence, public feelings of insecurity and a lack of faith in officials -- the report paints a picture of a mission far from complete.
"Although the security situation continues to improve, the Afghan government must continue to make progress toward key governance and development initiatives for security gains to become sustainable," the report says.
The time period covered in the document includes high-profile attacks including the September attacks on the U.S. Embassy and NATO headquarters in Kabul, fresh demonstration of what the report labels as "insurgent determination" to target the capital region.
"Nevertheless, these attacks were operational failures," the report says. "And the ANSF (Afghan National Security Forces) responded quickly and efficiently, demonstrating their growing capacity and ability to assume security lead in the transitioning areas."
Some of the strongest language is focused on the safe havens in Pakistan, with the report labeling them the insurgency's greatest enabler. They have become more important as American and coalition forces have cleared insurgents' hotbeds inside Afghanistan.
The report says that the successful U.S. raid by Navy SEALS on the Osama bin Laden compound in May, and recent indirect fire by the Pakistan military across the border, have led to a further deterioration of Afghan-Pakistani cooperation.
The report notes that major attacks were carried out by the Pakistan-based Haqqani network, deemed a terrorist organization by the United States.
"Addressing insurgents emanating from Pakistan is critical to the success of ISAF's campaign and Afghanistan's future," the report says. "ISAF will continue to assist Pakistan in denying Taliban and Haqqani safe haven from which they can plan and conduct attacks."
At the end of September, the United States had almost 98,000 military personnel in Afghanistan, and international partners had 46,400. But the Afghan public continues to worry about their security.
"Since April 2011, overall Afghan perceptions of security worsened slightly," the report says. "This is likely due to the increase in combat operations due to the summer fighting season as well as the Afghan population's perception of decreased freedom of movement due to insurgent-emplaced IEDs, the number one cause of civilian casualties in Afghanistan."
The report reminds American taxpayers that even after the U.S. military withdraws by 2015, there will be substantial bills to pay for Afghanistan security forces. So far the United States has provided the largest share of costs for police and other forces, while the international community also has contributed. "Nonetheless, the United States will likely continue to provide the preponderance of funding the ANSF for the foreseeable future," the report said.
Corruption continues to be a central concern, both for the U.S. and Afghanistan residents.
"During the reporting period, the Afghan government made only limited progress in building the human and institutional capacity for sustainable government," according to this latest study. "Despite continued U.S. and coalition support, the Afghan government continues to lack the resolve to address many corruption issues."
And despite insistence by the Afghanistan government that local firms take on jobs now performed by outside security firms, the Defense Department report suggests that it will be impossible to meet a March 2012 timetable because of a variety of training and logistics failures.