The Haqqani network — a family-run syndicate that happens to be one of South Asia’s most fearsome militant groups — has long been a source of tension for the volatile U.S.-Pakistan relationship. And it’s easy to understand why.

U.S. military officials often describe the Haqqani network as one of its biggest threats in Afghanistan. John Allen, who commanded U.S. and NATO forces in Afghanistan from July 2011 to February 2013, says the group wounded or killed more than 500 of his troops. It’s been blamed for an attack on the U.S. embassy in Kabul. It held Bowe Bergdahl, the only U.S. POW in Afghanistan, in captivity. It has close associations with Al-Qaeda, and the State Department has formally designated it as a terrorist organization (this status does not apply to the Afghan Taliban, with which the Haqqani network is affiliated).

The Haqqani network also has links to Pakistan’s security establishment, which views the group as a strategic asset that limits the influence of archrival India in Afghanistan (it frequently assaults Indian targets in Afghanistan). In 2011, Mike Mullen, then the Chairman of the Joint Chiefs of Staff, infamously described it as a “veritable arm” of Pakistan’s main intelligence agency. An angry Pakistan rejected the accusation and threatened to cut off ties with Washington.

Last year, unknown gunmen assassinated Nasiruddin Haqqani, one of the group’s top leaders. Tellingly, he was not gunned down in an isolated, mountainous, tribal-area redoubt — but rather as he strolled into a bakery in the suburbs of Islamabad, Pakistan’s capital (Rawalpindi, the city that houses military headquarters, is nearby).

For years, Haqqani fighters enjoyed a sanctuary in Pakistan’s North Waziristan tribal agency. Washington (to the irritation of Islamabad) pressured Pakistan relentlessly to target this safe haven, but to no avail.

Then, in recent weeks, Pakistan changed course and launched a military offensive in North Waziristan. Islamabad insists that its offensive is targeting all militant groups, including the Haqqani network. Pakistani officials report that the offensive has driven the group into Afghanistan, and they are asking U.S. forces to go after it there. In effect, Pakistan wants the United States, and its Afghan allies, to serve as the anvil to Pakistan’s hammer.

This should all be music to Washington’s ears. Unfortunately, it is not. That’s because the offensive is happening several years too late, and because there’s little reason to believe Pakistan’s claims about targeting the Haqqani network are actually true. As a result, U.S.-Pakistan relations face a new crisis rooted in an old problem.

Had Pakistan’s North Waziristan operation been launched several years earlier, at the height of the U.S. military surge in Afghanistan, then U.S. forces would have been in a strong position to handle an influx of fighters from Pakistan. Yet today, U.S. forces are headed for the exits.

Afghan troops aren’t in much of a position to help either. They have their hands full with a resurgent Taliban, which is staging stepped-up assaults. These have produced offensives in Helmand and Kandahar provinces and actual takeovers of territory in areas outside the cities of Kabul and Jalalabad. Some might argue that Pakistan’s North Waziristan offensive, by unloading Haqqani network fighters into Afghanistan, is contributing to this increased unrest in Afghanistan. The Afghan government, for its part, has blamed the Haqqani network for two recent major attacks — a mass-casualty market bombing and an assault on Kabul’s airport.

In effect, at the very moment U.S. forces are seeking some semblance of a smooth withdrawal from Afghanistan, a Pakistani military offensive is flushing some of the most ruthless anti-Afghan militants into that nation amid an intensified insurgency.

And it could get even worse.

Many Pakistani Taliban (TTP) fighters are based in eastern Afghanistan. The TTP (which mainly attacks the Pakistani state) and Haqqani network may focus on different targets, but they each share the same hardline ideology and loyalty to Afghan Taliban leader Mullah Omar. This all suggests that Haqqani fighters could conceivably cooperate operationally with TTP (and Afghan Taliban) forces in Afghanistan. Incidentally, one of the TTP’s founding leaders, the late Baitullah Mehsud, was once a Haqqani network commander.

At the same time, there’s little reason to believe Pakistan’s security establishment truly wants to take on its long-time trusted asset. Why would it want to sever ties now, given the uncertainties of Afghanistan’s future amid the U.S. withdrawal, and given that reconciliation with India remains a distant dream?

There’s also little reason to believe Pakistan wants the Haqqani network to stay out of Pakistan. The latter derives leverage over the Haqqani network by hosting it on its soil. By denying it a sanctuary, Pakistan would lose this leverage — and risk having the organization turn on the Pakistani state. Consider that some Afghan Taliban members have expressed deep unhappiness about Pakistan, and that when Baitullah Mehsud was a Haqqani commander, the group launched several attacks on the Pakistani military.

Little wonder, then, that a range of sources — from U.S. officials to North Waziristan locals — believe the Haqqani network was tipped off about the offensive by the Pakistani military and fled in advance. Pakistan’s own ambassador to Washington admits that many Haqqani fighters left North Waziristan before the offensive (in his view, this is simply because the operation was pre-announced).

So, despite all the spin about taking definitive action against militants of all stripes, Pakistan may have more nefarious objectives in North Waziristan: Smash the sanctuaries of anti-state militants such as the TTP, but shield the Haqqani network by sending it to Afghanistan (and to other Pakistan tribal areas), where the group can exploit rising political instability (stemming from an ongoing election crisis) and aid an increasingly emboldened Afghan Taliban. Then, when the offensive in North Waziristan has ceased, the organization can return to its Pakistani sanctuary and resume its cross-border strikes on Afghanistan.

This all has troubling implications for U.S.-Pakistan relations. Washington can’t be happy that Pakistan is merely displacing, rather than destroying, the Haqqani network — and especially into Afghanistan at such a delicate time. If the Haqqani network returns to its North Waziristan sanctuary and resumes attacks on Afghanistan, threats will likely intensify on Capitol Hill to reduce military aid to Pakistan. After all, a recent U.S. defense spending bill calls for $300 million in military aid to be withheld from Pakistan if the country has not “significantly disrupted” the Haqqani network’s “safe haven and freedom of movement.”

Such warnings won’t be received well in Islamabad, where officials often (and justifiably) note that Pakistan’s military has lost scores of soldiers fighting militant groups in the tribal belt, and complain that U.S. forces have failed to disrupt Pakistani Taliban safe havens in Afghanistan, which are used to mount attacks on Pakistan. Indeed, some of the TTP’s most vicious and hardline leaders — including supreme leader Mullah Fazlullah, who orchestrated the brief takeover of the Swat region in 2009, and TTP Mohmand tribal agency chief Omar Khalid Khorasani, who earlier this year ordered the execution of 23 Pakistani soldiers held in captivity — are reportedly based in Afghanistan.

The upshot? The current period of preternaturally placid U.S.-Pakistan relations could soon be shattered, thanks to the militant organization that so often bedevils them.

Michael Kugelman is the senior program associate for South Asia at the Woodrow Wilson International Center for Scholars in Washington, DC. He can be reached at [email protected] or on Twitter @michaelkugelman.