US Secretary of State Hillary Clinton has already cancelled one meeting and the diplomatic row threatens talks due later this month on the war in Afghanistan.
The freeze comes as a damning US watchdog report reveals that aid money lavished on Pakistan – almost $4bn since 2009 – as part of a strategy to foster closer ties has failed to show any change.
The case of Raymond Davis has convulsed Pakistan, opening a fresh seam of anti-American anger and unleashing a wave of speculation about what an American diplomat was doing driving alone in a Honda Civic through the streets of Lahore with a Glock handgun.
Pakistan has so far refused to release Davis despite US insistence that he is entitled to diplomatic immunity.
The US has warned Pakistan that it would consider cutting aid unless Davis is freed.
Buck McKeon, chair of the House Armed Services Committee, said he mentioned to Pakistani leaders that Congress was working on the budget.
Asked if aid could be at risk, Mr McKeon said: “It very well could be.”
A senior Pakistani official said the government had to balance its international commitments with the risk of provoking a backlash if it was seen to bow to Washington's pressure.
"We understand that diplomatic immunity is absolute. It's not that we don't get it," he said. "Pakistanis have been killed and there is a lot of emotion on the ground so all the Pakistani government is seeking is American understanding."
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He confirmed that ministerial-level talks had been frozen.
Last week, Mrs Clinton cancelled a meeting with Shah Mehmood Qureshi, Pakistan's foreign minister, at an international security conference in Munich. The two are due to meet again in Washington on February 24, along with their Afghan counterparts.
The freeze is the latest setback in relations between two countries that have maintained an awkward alliance against al-Qaeda and Taliban fighters along the Pakistani border with Afghanistan.
Davis has been held for 12 days since shooting two men whom he claimed were trying to rob him. A third man died after being run over by a vehicle sent to rescue the American.
A massive five-year civilian aid package was meant to help stabilise the nuclear-armed country, quell rampant anti-American feeling and prove to Pakistanis that the US was not simply using the country to do its dirty work against the militant threat.
However, the inspectors general's report found that USAID had failed to come up with a set of indicators to monitor progress.
It also revealed that one fifth of posts – or 68 jobs – remained unfilled in USAID's office in Islamabad.
A key priority was to promote economic development in Pakistan's tribal areas as a way of reducing the influence of extremist groups but that has also struggled to make an impact.
"The audits found the programmes had made little progress in achieving the goal largely because of the hostile environment – the chief of party for one implementing partner was assassinated – but also because of a lack of baseline date and inadequate oversight, which resulted in questioned costs of $767,841," the report said.