“If the parliament opens land routes for the NATO troops, we will target members of parliament and their party leaders,” Tehrik-e-Taliban Pakistan spokesman Ehsanullah Ehsan said.
“We are aware that the pro-American parliamentarians have started efforts to legalize routes to NATO forces,” Ehsan said in a statement.
He said the parliamentarians should know that they “would not be safe in their homes” if they backed the reopening of the supply routes.
Ehsan asked drivers not to transport supplies for NATO troops.
“We will publicly slaughter drivers who carry supplies for NATO forces,” he warned.
“The Pakistan Army and the rulers are bent on destroying the country and the Taliban are working for a new Pakistan,” Ehsan said.
He claimed the country's leaders had sold their conscience to the Americans and “whatever they are doing for the US is shameful”.
Pakistan closed all the supply routes after a cross-border NATO air strike on two border posts killed 24 Pakistani soldiers in November.
The parliament will on Monday begin a debate on Pakistan's future relationship with the US and new terms of engagements with the US and NATO in Afghanistan.
Parliamentarians will also decide whether to recommend the reopening of the supply routes to the government.
The Parliamentary Committee on National Security has recommended that the supply lines for NATO troops should be restored after imposing a tax on container trucks and oil tankers.