The US has quietly decided to release more than $1.6bn (£1bn) in military and economic aid to Pakistan that was suspended when relations between the two countries disintegrated over the covert raid that killed Osama bin Laden and deadly US air strikes against Pakistani soldiers. Officials and congressional aides said ties have improved enough to allow the money to flow again.

US and Nato supply routes to Afghanistan are open. Controversial US drone strikes are down. The US and Pakistan recently announced the restart of their "strategic dialogue" after a long pause. Pakistan's new prime minister, Nawaz Sharif, is travelling to Washington for talks this coming week with President Barack Obama.

But in a summer dominated by foreign policy debates over the coup in Egypt and chemical weapons attacks in Syria, the US has not promoted its revamped aid relationship with Pakistan. Neither has Pakistan.

The silence reflects the lingering mutual suspicions between the two.

The Pakistanis do not like being seen as dependent on their heavy-handed partners. The Americans are uncomfortable highlighting the billions provided to a government that is plagued by corruption and perceived as often duplicitous in fighting terrorism.

Congress has cleared most of the money, which should start moving early next year, officials and congressional aides said.

Over three weeks in July and August, the State Department and the US Agency for International Development informed Congress that it planned to restart a wide range of assistance, mostly dedicated to helping Pakistan fight terrorism. The US sees that effort sees as essential as it withdraws troops from neighbouring Afghanistan next year and tries to leave a stable government behind.

Other funds focus on a range of items, including help for Pakistani law enforcement and a multibillion-dollar dam in disputed territory.

US-Pakistani relations have weathered numerous crises in recent years. There was a months-long legal battle over a CIA contractor who killed two Pakistanis, in addition to the fallout from Bin Laden's killing in the Pakistani military town of Abbottabad in May 2011. The Pakistani government was outraged that it received no advance warning of the Navy Seal raid on Bin Laden's compound.

Adding to the mistrust, the US mistakenly killed two dozen Pakistani soldiers in November 2011. Islamabad responded by shutting land supply routes for troops in Afghanistan until it received a US apology seven months later.

The State Department told Congress that the US had not conducted any significant military financing for Pakistan since the "challenging and rapidly changing period of US-Pakistan relations" in 2011 and 2012. The department stressed the importance now of enhancing Pakistan's anti-terrorism capabilities through better communications, night vision capabilities, maritime security and precision striking with F16 fighter jets.

The department told Congress on 25 July that it would spend $295m to help Pakistan's military. Twelve days later it announced $386m more. A pair of notifications arriving on 13 August and worth $705m centred on helping Pakistani troops and air forces operating in the militant hotbeds of western Pakistan, and other counterinsurgency efforts.

The administration had until the end of September to provide Congress with "reprogramming" plans at the risk of forfeiting some of the money, which spans federal budgets from 2009-2013.

State Department officials said the renewal of aid was not determined by any single event. But they noted a confluence of signs of greater cooperation, from Pakistan's improved commitment to stamping out explosives manufacturing to its recent counterterror offensive in areas bordering Afghanistan that have served as a primary sanctuary for the Taliban.

The officials spoke on condition of anonymity because they were not authorised to talk publicly about the aid relationship ahead of Sharif's visit. They said the money would start reaching Pakistan in 2014 but take several years to disburse fully.

In its notifications to Congress, the department described fighting terrorism as a mutual concern but said little about the will of Pakistan's government, army and intelligence services to crack down on militant groups that often have operated with impunity in Pakistan while wreaking havoc on US and international forces across the border in Afghanistan.

Top American officials have regularly questioned Pakistan's commitment to counterterrorism. In 2011, Admiral Mike Mullen, then chairman of the Joint Chiefs of Staff, described the militant Haqqani network as a "veritable arm" of Pakistani intelligence. Lawmakers and administration officials have cited Pakistani support for the Taliban, Lashkar-e-Taiba and other militant groups. In September, the administration sent officials from multiple agencies for closed-doors briefings with the House and Senate foreign relations committees, officials and congressional aides said.

The House Foreign Affairs Committee has cleared all of the notifications. The Senate Foreign Relations Committee is reviewing a $280m chunk of military financing, Senate aides said. Aides spoke on condition of anonymity because they were not authorised to talk publicly on the matter.

While Washington has publicly challenged Islamabad to step up its fight against militant groups, Pakistan's biggest complaint has been the huge surge in drone strikes on terrorist targets, which Pakistanis see as violations of their sovereignty. The number of attacks has dropped dramatically this year.

The countries say they are now moving past the flaps and mishaps that soured their partnership in recent years. During an August trip to Pakistan, the secretary of state, John Kerry, announced the restart of a high-level "strategic dialogue" with Pakistan on fighting terrorism, controlling borders and fostering investment.

Among the economic aid programmes included in the US package, support for the Diamer-Basha dam near Pakistan's unresolved border with India has the potential for controversy and tremendous benefit.

Pakistan's government has been unable to secure money for the project from the World Bank, and the Asian Development Bank is waiting to hear from the United States and India before providing financing to help construction. The dam faces massive funding shortfalls.

In its 24 July notification to Congress, USAID said the project could cost up to $15bn and take a decade to complete. The agency promised only to provide "financial and technical assistance" for studies, including on environmental and social aspects, while expressing hope the dam could be transformative for a country with chronic power shortages. State Department officials put the bill for the studies at $20m.

If the dam were ultimately built, USAID wrote, it could provide electricity for 60 million people and 1m acres of crop land, and provide a ready supply of water for millions more. It noted that Pakistani officials have sought American support at the "highest levels".

Despite amounting to just a small portion of the overall US aid package, congressional aides said Pakistan's government has lobbied particularly hard for the dam money to be unlocked.

Pakistan's embassy in Washington refused to comment on the aid or say if Sharif would bring up any specific programmes in talks at the White House.