Police say at least three people were killed when gunmen opened fire on the tankers and then set the trucks ablaze at a depot in Islamabad before dawn.
A Pakistani Taliban spokesman told reporters that the attacks would continue until the supply convoys are stopped. The militant group also said it was avenging drone strikes on Pakistani territory.
A second attack took place Monday in the southwestern province of Baluchistan. Pakistani officials say two gunmen on motorcycles torched two trucks carrying NATO supplies, killing one person.
Meanwhile, NATO supply convoys remained lined up at the Torkhum border crossing in northwestern Pakistan, four days after it was shut following a NATO cross-border raid that Pakistan says killed three of its soldiers in the Kurram region.
NATO Secretary-General Anders Fogh Rasmussen expressed his regret for the soldiers’ deaths during talks Monday with Pakistani Foreign Minister Shah Mehmood Qureshi in Brussels. Rasmussen also urged Pakistan to reopen the supply route as soon as possible.
Pakistani officials say they closed the Torkhum border crossing for security reasons.
On Sunday, Pakistan’s ambassador to the United States indicated the supply route would reopen this week.
The border crossing along the Khyber Pass is on one of the main NATO supply routes through Pakistan into Afghanistan, where more than 152,000 U.S. and NATO personnel are fighting a Taliban-led insurgency.
NATO says its forces were pursuing militants out of self defense when helicopters crossed the border into Pakistan on Thursday. A joint investigation is underway.
A sharp increase in attacks by unmanned planes flying over Pakistan and recent NATO border incursions have raised tensions between the international forces and Islamabad.
Some information in this story was provided by AP, AFP and Reuters.