Authorities from the Baltic state received a report on Tuesday that the soldiers had disappeared during a military drill on a training ground in the eastern city of Pabrade, near the border with Belarus.

Search and rescue teams used heavy equipment and excavators to remove silt from the body of water where the vehicle was located and managed to attach cables to tow it out of the swamp.

"The vehicle has been recovered," Lithuanian Armed Forces chief General Raimundas Vaiksnoras said on Monday morning on social media.

"I ask for everyone's respect and solidarity as we await further information from our US colleagues," Vaiksnoras added.

Lithuania's Defence Minister Dovile Sakaliene said that the towing operation was completed at 4:30 am local time (0130 GMT) and that the Lithuanian Military Police and US investigators were "currently working at the scene".

"If the recovery of the vehicle does not provide all the answers, the work will have to continue," she added in a Facebook post.

Hundreds of local and foreign troops and other rescue workers including engineers and divers had been involved in a rescue operation to recover the M88 Hercules armoured recovery vehicle.

Lithuania, a NATO and EU member, hosts more than 1,000 American troops stationed on a rotational basis.