"This house demands investigation and punishment for those who were responsible for this deplorable act," the resolution said.
"Nato will have to take steps to stop such irresponsible acts in the future," added the resolution, presented by Nayyar Bukhari, leader in the Senate from Pakistan People's Party (PPP).
Violent anti-US protests over the Holy Quran burning killed 40 people in Afghanistan, plunging relations between Nato members and their Afghan allies to an all-time low and forcing US President Barack Obama to apologise.
Protests also spilled over into Pakistan, where the resolution was passed at a farewell session for the outgoing Senate.
Pakistan's parliament is tentatively expected to review Pak-US relations later this month at a joint session that has been repeatedly delayed.
The review is considered key to getting Pak-US diplomatic relations onto a more solid footing after US air strikes killed 24 Pakistani soldiers on November 26 and brought the relationship to its lowest point in years.
The killings capped a disastrous year for an alliance already seriously compromised by a covert raid to kill Osama bin Laden on May 2 and the detention of a CIA contractor who killed two Pakistanis in January 2011.
Islamabad closed its border crossings to Nato supplies and ordered US personnel to leave the Shamsi airbase, reportedly a hub for covert American drone strikes against the Taliban and al Qaeda in Pakistan's tribal belt.
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