WASHINGTON: The US has carried out a series of airstrikes in recent days against some of Pakistan's most wanted militants hiding in a remote border area, the latest sign of improving relations between the two reluctant allies after years of recrimination following the 2011 raid in Pakistan that killed Osama bin Laden.

On Nov 24, an American airstrike in eastern Afghanistan narrowly missed Pakistani Taliban leader Mullah Fazlullah, a top target for Pakistan's military and the leader believed to have ordered the attack on schoolgirl Malala Yousafzai, a US official said.

The official was not authorised to be quoted by name discussing the clandestine operation. Col. Brian Tribus, spokesman for the international coalition in Afghanistan, said the strike also killed three armed militants in Afghanistan's Nangarhar province.

The operation was one of a recent series along the Afghanistan-Pakistan border aimed at the group known as the Tehreek-i-Taliban Pakistan, according to US officials who were not authorised to be quoted by name discussing the strikes.

While the State Department considers that group a terrorist organisation, it poses a far greater threat to Pakistan than to the United States, having killed thousands of Pakistanis.

The US airstrikes are the latest indication that the US-Pakistan counter-terrorism alliance has recovered from the serious breach it suffered after Al Qaeda leader bin Laden was found hiding in Pakistan in 2011 and the US launched a secret operation to kill him without telling Pakistan in advance.

While neither government fully trusts the other, the relationship has fallen back into its old equilibrium of wary cooperation, according to several American military, diplomatic and intelligence officials who declined to be quoted discussing the sensitive topic.

The counter-terrorism alliance is considered crucial to the future of Afghanistan and the effort to destroy Al Qaeda. As it has for years, the US continues to accuse elements of the Pakistani government of secretly supporting terrorists who may serve its interests in Afghanistan.

But the US also provides Pakistan more than $2 billion a year in military and economic aid, and the countries work closely on some counter-terrorism matters.

“US-Pakistani military cooperation is on the upswing after a long period of tense dysfunction,” said Democratic Rep. Adam Schiff, who serves on the House Intelligence Committee.

“We are on a much better trajectory,” said a senior Pakistani military official who was not authorised to speak by name, but was expressing what he said was a widely held view in his government.

After a six-month pause while the Pakistan government pursued peace talks with the Pakistani Taliban, the CIA in June resumed drone strikes in Pakistan's tribal areas near the Afghan border.

That policy is opposed by Pakistanis concerned about civilian casualties and the compromise of their sovereignty. But the pace of attacks is much slower than it used to be, and no civilian deaths have been confirmed in the 20 strikes recorded since, according to two organisations that track media reports of the attacks.

Criticism in Pakistan has been far more muted than it once was. The Pakistani military, meanwhile, this year conducted a major offensive against militants in the tribal region of North Waziristan, clearing a town, Miramshah, that once was a headquarters for the Haqqani network.

It was a move that had been demanded for years by the US government, which has accused Pakistan of playing a double game by fighting militants who threaten Pakistan while secretly backing those who threaten only Afghanistan and the US American officials and outside. Analysts say Pakistan supports the Haqqanis and other military groups as a way of retaining leverage over Afghanistan, where Pakistan's rival, India, wields significant influence.

Several US officials said in interviews that the double game continues, because key Haqqani leaders were warned in advance about the offensive and decamped to Pakistani cities.

Pakistan denies giving warnings. Either way, American military leaders in Afghanistan say the Pakistani army push has disrupted Haqqani operations and bodes well for future cooperation.

The Pakistan operation in North Waziristan has “fractured” the Haqqani network, Lt. Gen. Joseph Anderson, the deputy commanding general of US forces in Afghanistan, told reporters in November.