The contractor, Raymond Davis, shot dead two men in the eastern city of Lahore last month. He said he acted in self-defense and the United States says he has diplomatic immunity and should be repatriated.
The case has inflamed anti-American sentiment in Pakistan and is straining relations between the allies. Pakistani efforts against Islamist militants on its border with Afghanistan are seen as crucial to ending the war in neighboring Afghanistan.
"He (Davis) said that he should be given immunity ... a discussion will be held on this at the next hearing," said Asad Manzoor Butt, a lawyer for the families of the two men Davis killed.
Davis, a former U.S. special forces officer, has been charged with double-murder and faces possible execution.
There have been conflicting accounts about the identity of the two victims with Davis and a police report indicating they were armed robbers while Pakistani media and some officials have portrayed them as innocent victims.
With public anger and anti-American feeling running high, President Ali Asif Zardari's unpopular government had little choice but to let the case go through the courts.
"He should be treated the same way he treated Pakistanis," said Muzammil Mukhtar, a laborer in a factory near Kot Lakhpat jail, where Davis has been detained since February 11 and where his trial began on Friday.
"We should not care about our relations with America. These have never been good."
Davis is being held under tight security.
Protesters have burned effigies of him and U.S. flags since details of the killings became public, sparking concern about his safety.
U.S. Consul General General Carmela A. Conroy attended the trial, but reporters and other members of the public were not allowed in.
The murder trial is one of two legal cases involving Davis.
On March 14, a Lahore court will decide whether he enjoys diplomatic immunity, another contentious issue that the government has said must be decided legally, at the risk of angering the United States and jeopardizing up to $3 billion a year in U.S. military and civilian aid.
"Davis case is not so simple as it is sometimes portrayed by some. It is a complex case involving issues in national and international law as well as grave sensitivities that cannot be wished away," presidential spokesman Farhatullah Babar said.
"The court has not only taken cognizance of it but also declared that it will decide on the immunity issue. We respect the court and will wait for its verdict."
In addition to causing a diplomatic standoff, the case has strained, but not broken, relations between the CIA and Pakistan's main Inter-Services Intelligence (ISI) spy agency, which did not know of the presence of Davis in the country.
CIA-ISI ties are essential to battling al Qaeda and Taliban militants in Pakistan and neighboring Afghanistan, where U.S. and other foreign forces are fighting an almost decade-old war that has become increasingly bloody.
Relations between the spy agencies took a blow in December, when the CIA station chief in Islamabad was forced to leave the country after his name was published in a court filing over attacks in Pakistan by pilotless U.S. aircraft.
The latest case has made things worse, as even the usually tight-lipped ISI noted.
"Post incident conduct of CIA has virtually put the partnership into question ... it is hard to predict if the relationship will ever reach the level at which it was prior to the Davis episode," the ISI said in a letter to the Wall Street Journal last week.
The United States says it holds Pakistan responsible for the safety of Davis, and prison sources say his cell is in an area isolated from other prisoners and under constant surveillance and heavy guard.
There is reason for worry in Pakistan, where rogue security forces have at times turned on government officials.
Last month, Punjab province Governor Salman Taseer was shot dead by one of his own guards. His killer became a hero for Islamist groups that opposed the governor's moderate political views.
(Additional reporting by Mian Khursheed, Arshad Mohammad and Sheree Sardar; Writing by Rebecca Conway and Chris Allbritton; Editing by Robert Birsel)
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