Dovile Sakaliene said she could not confirm whether the soldiers, who had been in Lithuania for two months, were inside the vehicle found submerged in a body of water on Wednesday.
Lithuanian authorities received a report on Tuesday about the soldiers' disappearance during a military drill on a training ground in the eastern city of Pabrade, which is near the border with Belarus.
"All scenarios are still being considered... We can't confirm whether the soldiers are inside the vehicle," Sakaliene told reporters at the scene.
"The Americans informed us that they also continued searching throughout the night in the surrounding area, as any scenario is still possible until we see the vehicle."
Local and foreign troops, along with helicopters from the air force and the state border guard service, have been deployed to search for the soldiers.
Poland's Defence Minister Wladyslaw Kosiniak-Kamysz said on Thursday the NATO member was sending "dozens of soldiers with heavy equipment and divers" to help the search.
Lithuania, a NATO and EU member, hosts more than 1,000 US troops stationed on a rotational basis.
The US Army said on Wednesday that the M88 Hercules armoured recovery vehicle operated by the soldiers was "discovered submerged in a body of water in a training area".
US Army Europe and Africa's public affairs office added that the soldiers "were conducting scheduled tactical training at the time of the incident".
Sakaliene said the vehicle weighs several dozen tonnes and is about five metres (16 feet) deep in mud, adding that the location was "a swamp connected to a lake".
"In 24 hours, a new road has actually been built so heavy equipment can arrive. The water level has also been lowered enough to begin excavation work," she added.
She said the situation was made more difficult by a gas pipeline running through the area, where hundreds of people have been working as part of the search and rescue operation.
"It's very hard to say exactly how long this will take," she said.
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