36-year-old 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 his claim of self-defence and booked him for murder.
Lahore High Court Chief Justice Ijaz Ahmed Chaudhry, who was due to rule on Davis' claim of diplomatic immunity, said the issue would be decided by the Additional District and Sessions Court that is conducting the US national's trial on murder charges.
"The matter about immunity will be decided by the trial court," Chief Justice Chaudhry said in his order.
Legal experts said the High Court's decision is expected to extend the crisis triggered by Davis' arrest and complicate efforts by Pakistan and the US to resolve the matter.
Deputy Attorney General Navid Inayat Malik, who appeared in the High Court on the government's behalf to file the Foreign Ministry's response in the case, said Davis had come to Pakistan on an official business visa requested by the US government.
After Davis' arrest, the US Embassy told the Pakistan government that he had been issued a diplomatic passport and thus had diplomatic immunity, Malik said.
The Foreign Ministry's response did not give any clear answer on Davis' diplomatic status.
The Chief Justice then gave his ruling and disposed of four similar petitions that had asked the High Court to direct the government not to hand over Davis to the US.
Additional District and Sessions Judge Yousuf Aujla, who is conducting Davis' trial on murder charges, had on March 3 rejected the American's claim of diplomatic immunity and said he would go ahead with the trial.
The hearing on the murder charges will resume on Wednesday.
Pakistan's top leadership, fearful of a public backlash due to rising anti-American sentiments, has rebuffed repeated US demands for Davis to be freed on grounds of diplomatic immunity and said that the matter must be decided by the courts.