Pakistani Taliban spokesman Ahsanullah Ahsan accused officials of acting like slaves for the US and said allowing Nato supplies to resume would be "shameful and unacceptable."
"These parliamentarians must know that in such case, none of them will be safe in their homes," Ahsan told The Associated Press. "We will start attacking all the parliamentarians and their families."
Ahsan also said militants would "publicly slaughter" drivers ferrying Nato supplies.
The US is eager to get the supplies moving again because it has had to spend much more money shipping goods by an alternative route that runs through Central Asia.
The supply line through Pakistan will also be key to trucking out equipment as the US seeks to withdraw most of its combat forces from Afghanistan by the end of 2014.
A parliamentary commission tasked with proposing new guidelines for the relationship between the two countries last week demanded an end to American drone attacks and an apology for the airstrikes that killed Pakistani troops.
The commission also recommended that the Pakistani government charge Nato more for shipments through the country if it allows them to resume. The parliament is scheduled to begin debate on these points Monday.
Washington has expressed regret for the border incident but avoided a formal apology. US officials were reportedly preparing to apologise last month but had to postpone the plan after US soldiers burned copies of the Quran in Afghanistan. President Barack Obama apologised for that, bring criticism from political opponents.
Prime Minister Yousuf Raza Gilani is scheduled to meet Obama during a meeting in Seoul, South Korea, on Tuesday.
The army, and to a lesser extent the civilian government, will ultimately decide whether to restore ties with the US, but parliament could influence the decision. Analysts say placing the issue before lawmakers is an attempt to give the government and the army some political cover, so they can claim support of the country before quietly reopening the supply route.
Opposition lawmakers have indicated they may not back the proposed new terms with the US.