Judge Vladislav Lencik of Vilnius Regional Court gave his ruling after hearing arguments of both sides and an explanation by a specialist from the Ministry of National Defense. According to the judge, prosecutors' request was legitimate and should be satisfied.
The ruling is not final and can be appealed within seven days to the Court of Appeal of Lithuania.
Issuing his ruling, the judge drew attention to the fact that it was not about the person's guilt but on whether the Criminal Code of Lithuania provided for circumstances under which a person could not be extradited.
"Having looked into the submissions, the court rules that the information provided is enough to claim that he could have carried out criminal acts identified in the US request," the judge said, rejecting Ustinov's claims that he is being persecuted for his Russian citizenship.
Judge Lencik called Ustinov's claims declarative and unsubstantiated.
Ustinov was present at the hearing. He was not accompanied by his lawyer.
In an effort to assist colleagues from the United States, Vilnius officers detained the Russian citizen wanted by the US state of Delaware at Vilnius International Airport in May.
The Russian national, 46, was detained after arriving to discuss the purchase of night vision devices banned in the US. The man is suspected of having exported weapons on the US list of defense weapons to Russia, paying hundreds of thousands of US dollars for the items.
Ustinov is currently held at Vilnius Lukiškės Remand Prison after a pre-trial judge ordered his arrest for two months.
The extradition request was received from the US last month.
Lithuanian officials had been asked to detain Ustinov by the US Justice Department after it received information that Ustinov might flee to Russia via Lithuania.
Ustinov was charged in the US on March 25. He is suspected to have exported or attempted to export weapons on the US defense weapons list without having an export permit, smuggled weapons and laundered illegally-gained money.
Ustinov is facing at least 20 years in prison in the US.