Previous drafts of the deal have only agreed that US troops can be held accountable under Iraqi law for any crimes committed outside their bases while off duty.
Baghdad has also sought to ensure that the US military does not use Iraqi territory as a base to launch attacks on neighbouring countries.
As the cabinet debated the pact, three people died after a homemade explosive device went off near a checkpoint in Baghdad, police said.
Two members of so-called "Awakening" group, Sunni fighters who have allied with US forces to take on al-Qaeda, were among the dead.
Seven other people were wounded in the attack, police said.
Many Iraqis have protested against the security deal, with thousands of people turning up at a recent opposition rally organised by Muqtada al-Sadr, an Iraqi Shia leader.
Ahead of the vote, Nuri al-Maliki, the Iraqi prime minister, dispatched Khalid al-Attiyah and Ali al-Adeeb, two senior Shia legislators to Najaf to secure the support of Grand Ayatollah Ali al-Sistani, the country's top Shia cleric.
The Iranian-born al-Sistani commands enormous influence with Iraq's Shia majority.
The Associated Press quoted a senior official at al-Sistani's office as saying the cleric told the prime minister's emissaries that the draft document represented "the best available option" for Iraq, signaling that he would not object to it if the cabinet and parliament approve it.
The deal is not expected to affect the pledge by Barack Obama, the US president-elect, that he would withdraw US troops from Iraq.
Reactions and concerns
Al-Attiyah said al-Sistani had stressed the need for "national accord" over the agreement.
"His eminence, al-Sistani, is comforted by the thoroughness of Iraqi officials who shoulder the responsibility of safeguarding national interests," Al-Adeeb said.
Many Iraqi legislators are concerned about appearing to endorse the US occupation ahead of upcoming provincial elections next year.
Al-Sadr has threatened to support attacks on US forces if they stay in Iraq.
Raed Jarrar, an Iraq analyst, told Al Jazeera that most Iraqis feel that the US-Iraqi deal will only further legitimise the US occupation of Iraq.
"This agreement is similar to the deal that Britain tried to impose on Iraq in 1937 when Britain was occupying Iraq. That deal was widely rejected," he said.
"We have had very strong statements by the Iraqi Islamic Party. Its leader, Tareq al-Hashimi [Iraq's vice-president], said he did not want the agreement to pass without an approval of the majority of Iraqis - he wants it to be part of the next elections where Iraqis can approve it through a referendum."
The UN mandate covering the presence of US forces in Iraq expires on December 31, and failure to pass the security agreement would leave Iraq with little choice but to seek a renewal of the mandate.