What might be the final major U.S. offensive of the Afghanistan war has begun, according to the war's day-to-day commander. Its purpose is a bit harder to grasp.

Lt. Gen. Curtis Scaparrotti, the outgoing operational commander in Afghanistan, said that US and Afghan troops recently began a push in the eastern province of Ghazni to reduce the potency of the insurgency in an area neglected by the 2010 troop surge.

"In some areas there in the east, south of Kabul, we needed to insert greater combat power, and we've needed to do that for quite some time," Scaparotti told Pentagon reporters via videoconference, contradicting remarks made by the general in charge of east Afghanistan last year. Led by an additional brigade from the 82nd Airborne, the offensive will last through "the current fighting season," he said – even as about 20,000 US forces withdraw by October, weeks before the fighting season ends.

Scaparrotti declined to provide details on how many forces make up what he described as "greater combat power"; where it goes beyond or outside of Ghazni; and said he preferred not discuss even the "intent" of the operations publicly. He also said not to think of it as the "last" major US offensive of the Afghanistan war. But it follows a recent pattern as NATO nears its 2014 deadline for turning Afghan security to its Afghan proteges: US and Afghan troops will clear areas in the east that the Afghans will be tasked with holding.

All Scaparrotti offered was that US forces were "now undertaking operations to secure areas in Ghazni and areas surrounding Ghazni that we've needed to do for some time, and we're also working very hard with our Afghan partners to then gain in strength and to hold those areas once these operations are done."

The military has hardly made a secret of its desire for one last major push into eastern Afghanistan. The Obama administration has hardly made a secret of its desire not to replicate the grueling troop surge, which focused on the south, in eastern Afghanistan. Last week, Gen. Martin Dempsey, the chairman of the Joint Chiefs of Staff, told reporters that another push into the east would be critical to eroding the power of the Haqqani Network, one of the most lethal components of the Afghan insurgency.

"We've got to get [eastern Afghanistan] and the Haqqani influence reduced in order to meet our timelines for the transition that we're moving toward and – at the end of '14," Dempsey said.

Scaparrotti, whose tour in Afghanistan ends Tuesday, diminished expectations for the offensive. He spoke about "future complementary operations" with the Pakistanis as little more than a hypothetical, rather than a partnered effort to squeeze the Haqqani network on both sides of the border. And Scaparrotti said he was optimistic that NATO would meet the 2014 timetable seemingly regardless of what happens in eastern Afghanistan.

The Haqqani Network is considered responsible for the recent wave of attacks on Kabul, although Scaparrotti said the offensive is focused "on the insurgency in a broad way," not just on the Haqqanis. But still, Scaparrotti said that Ghazni is the current heart of the effort, even though that's not a province the Haqqani Network evidently values.

According to the general, the Haqqanis want to defend three other provinces – what is "traditionally their area of operation: Khost, Paktia, and Paktika."

So what could well be the final major US campaign in Afghanistan doesn't initially target the terrain that its adversary most wants. It won't have the same access to air power that the effort to take Helmand and Kandahar enjoyed. It won't have complementary effort on the border by the Pakistanis to deny insurgent safe havens. And whatever happens won't change the timetable for handing over Afghanistan to the Afghans. No wonder the military isn't exactly playing up the fight for eastern Afghanistan.