WASHINGTON (NYTIMES) - When Pakistani forces freed a Canadian-American family this fall held captive by militants, they also captured one of the abductors.

US officials saw a potential windfall: He was a member of the Taleban-linked Haqqani network who could perhaps provide valuable information about at least one other American hostage.

The Americans demanded access to the man, but Pakistani officials rejected those requests, the latest disagreement in the increasingly dysfunctional relationship between the countries.

Now, the Trump administration is strongly considering whether to withhold US$255 million (S$340.80 million) in aid that it had delayed sending to Islamabad, according to US officials, as a show of dissatisfaction with Pakistan's broader intransigence toward confronting the terrorist networks that operate there.

The administration's internal debate over whether to deny Pakistan the money is a test of whether President Donald Trump will deliver on his threat to punish Islamabad for failing to cooperate on counter-terrorism operations.

Relations between the United States and Pakistan, long vital for both, have chilled steadily since the president declared over the summer that Pakistan "gives safe haven to agents of chaos, violence and terror".

The United States, which has provided Pakistan more than US$33 billion in aid since 2002, said in August that it was withholding the US$255 million until Pakistan did more to crack down on internal terrorist groups.

Senior administration officials met this month to decide what to do about the money, and US officials said a final decision could be made in the coming weeks.

The officials, who spoke on condition of anonymity to describe the sensitive discussions, did not detail what conditions Pakistan would have to meet to receive the aid. It was not clear how the United States found out about the militant's arrest, but a US drone had been monitoring the kidnappers as they moved deeper into Pakistan.

Ms Caitlan Coleman, an American, and her Canadian husband, Mr Joshua Boyle, were freed along with their children in an October raid after five years in captivity. Pakistani troops confronted Haqqani militants as they ferried the family across the tribal lands of north-west Pakistan.

The Trump administration has foreshadowed a cutoff in recent days with harsher language.

Last week, in announcing his national security strategy, Mr Trump again singled out Pakistan for criticism.

"We make massive payments every year to Pakistan," he said. "They have to help."

Vice-President Mike Pence reinforced that message in a visit to Afghanistan just before Christmas, telling cheering US troops that "President Trump has put Pakistan on notice".

The reaction of his audience was notable, analysts said, since the Pentagon has historically been one of Pakistan's defenders in Washington because of its long-standing ties to the Pakistani military.

Pakistan, however, has few friends in Mr Trump's National Security Council. Lt Gen H.R. McMaster, the national security adviser, served in Afghanistan, where he saw firsthand how Pakistan meddled in its neighbour's affairs. Ms Lisa Curtis, the council's senior director for South and Central Asia, brought critical views about Pakistan from her previous post at the conservative Heritage Foundation.

In a report she wrote in February with Mr Husain Haqqani, Pakistan's former ambassador to Washington, the two called for the administration to "avoid viewing and portraying Pakistan as an ally".

If Pakistan did not take steps to show its commitment to US counter-terrorism goals, they wrote, Mr Trump should strip it of its status as a major non-Nato ally.

Such a step would be more punitive than withholding the US$255 million in State Department assistance known as Foreign Military Financing, Mr Haqqani said in an interview, because it would deprive Pakistan of access to military equipment. He said Pakistani officials were bracing for some kind of aid cutoff.

Pakistan's military, he said, still views its accommodation of the Haqqani network as in its security interest.

To overcome that, the Trump administration would have to pursue other, more punishing measures, either by imposing targeted sanctions on the government or removing it from the list of non-Nato allies.

"Pakistan can withstand a cutoff in American aid," Mr Haqqani said. "It would have to be followed by something else to make Pakistan believe that Mr Trump means business."

In July, the Pentagon said it would withhold US$50 million in military reimbursements for Pakistan because the country had not taken "sufficient action" against the Haqqani network.

A State Department official said Pakistan's actions will ultimately determine the course of "security assistance in the future".

The official said conversations with Pakistan are continuing and declined to provide further comment.

The Pakistani government did not respond to a message seeking comment.

After Ms Coleman, Mr Boyle and their children were freed, the Pakistani military made no mention of the captured Haqqani operative.

Instead, the military released a statement saying the operation's "success underscores the importance of timely intelligence-sharing and Pakistan's continued commitment towards fighting this menace through cooperation between two forces against a common enemy".

Mr Trump said it was "a positive moment for our country's relationship with Pakistan".

US officials are eager to learn what the militant knows about Mr Kevin King, an American university professor who was kidnapped along with Mr Timothy Weeks, an Australian citizen, in August 2016.

Mr King is believed to be alive but ill and US officials are hopeful that he and Mr Weeks might be released.

Another American, Mr Paul Overby, vanished in 2014 in Afghanistan. Mr Overby was trying to interview the leader of the Haqqani network when he disappeared.

General Joseph L. Votel, head of the Pentagon's Central Command, which oversees Pakistan and Afghanistan, declined to provide any details on the Haqqani operative who was seized other than to say he was "probably pretty important" and that any militants involved in hostage-taking were "significant".

Gen Votel would not say whether the Trump administration is considering withholding aid from Pakistan to prod Islamabad to improve its counter-terrorism cooperation.

"What we're trying to do is to talk to Pakistan about this, and not try to communicate with them through public messaging," Gen Votel said in an interview.