During the last hearing of the case, Davis had filed an application in which he insisted that he had immunity.
Lawyers representing the families of the two men killed by Davis and the prosecution counsel today presented their arguments during proceedings conducted behind closed doors at Kot Lakhpat Jail by Additional District and Sessions Judge Yousuf Aujla.
After hearing the arguments of defence and prosecution lawyers, Judge Aujla said no legitimate document had been presented by Davis or the Pakistan government to show that the American had diplomatic immunity.
The judge said a note provided by the US Embassy was not sufficient to prove Davis` diplomatic status.
The judge rejected Davis` application claiming diplomatic immunity and said the court has the jurisdiction to go ahead with his murder trial.
When defence lawyers told the judge that they had not been provided all documents related to the charges levelled against Davis, Aujla directed the prosecution to ensure this was done and adjourned the case till March 8.
Lawyers representing the families of the two men killed by Davis said they expected the court to formally indict Davis at the next hearing.
Davis was represented at today`s hearing by three lawyers, including Zahid Hussain Bukhari, a former judge of the Lahore High Court.
US Consul General Carmela Conroy observed the proceedings that were held in the heavily guarded Kot Lakhpat Jail for security reasons. Davis is being held in the same prison.
At the last hearing, Davis refused to sign the charge-sheet that was given to him and insisted that he had immunity. He also contended that Pakistani courts could not take action against him.
In a separate case related to the charge of illegal possession of a gun, the judge extended the judicial remand of Davis by 12 days and adjourned the matter till March 15. This hearing too was held in Kot Lakhpat Jail.
Davis was arrested in Lahore on January 27 after he shot and killed two armed men he claimed were trying to rob him.
Police rejected Davis` claim that he acted in self-defence and have booked him for murder.
Pakistani leaders, including Prime Minister Yousuf Raza Gilani, have said the matter should be settled by the courts.
The case has been complicated by revelations that Davis was working as a security contractor for the CIA.
The Pakistan government has rejected repeated US demands for Davis to be freed on the grounds of diplomatic immunity and relations between the two countries have plunged to a new low.
On March 14, the Lahore High Court will hear a separate case to decide Davis` diplomatic status. The High court yesterday directed police to include media reports on Davis in their records.