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 were at the scene on Friday, using heavy military equipment and excavators to remove silt from the body of water where the vehicle had been located.
"I am still hoping for a miracle," Lithuanian President Gitanas Nauseda told reporters in Pabrade.
"Although many sceptics would probably say that there is nothing to hope for in these circumstances, I want to believe," he added.
The Lithuanian army later said on social media that they were "moving forward" on their goal to "turn the swamp into water so divers can jump in".
The US army said on Friday it was sending a specialised US Navy dive crew that was "expected to arrive on site within the next 24 hours".
Local and foreign troops, along with helicopters from the air force and the state border guard service, have been deployed in the search effort.
The M88 Hercules armoured recovery vehicle the missing US soldiers had been operating was found several metres deep in a swamp connected to a nearby lake.
"The area around the site is incredibly wet and marshy and doesn't support the weight of the equipment," US Army Europe and Africa's public affairs office said in a statement.
"Draining the area has been slow and difficult due to ground water seepage," it added.
"This will be a long and difficult recovery operation, but we are absolutely committed to bringing our soldiers home," said Curtis Taylor, Commanding General of the 1st Armored Division.
The main goal was to remove the mud from the submerged vehicle and identify possible attachment points for extraction, Lithuanian Armed Forces chief General Raimundas Vaiksnoras said.
Lithuania, a NATO and EU member, hosts more than 1,000 American troops stationed on a rotational basis.
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