"The first column of troops and combat equipment from the US Army's 3rd Cavalry Regiment crossed the Lithuanian border near Kalvarija at around 3 a.m.," the Lithuanian Armed Forces said.
The troops and equipment, including infantry fighting vehicles, armored SUVs and trucks, will be taking part in the Saber Strike drills in the Baltic states and Poland, it said.
They will initially train in Lithuania and then plan to go to Latvia.
"The exercise trains the tactical ability of the US forces to move capabilities into the eastern flank of NATO during the cold season and the interoperability with the Allies there," the Lithuanian military said in a press release.
Saber Strike 2022 is an element of the large-scale exercise Defender-Europe 2022.
The drills hosted by Lithuania will also involve the US 12th Combat Aviation Brigade and the Royal British Air Force troops with CH-47 Chinook transport helicopters and AH-64 Apache attack helicopters, as well as a US air defense platoon, according to the press release.
"The Polish troops with F-16 fighter aircraft and the British air personnel with Typhoon assets who are currently in charge of the NATO Air Policing Mission will be training in the Baltic skies too," it said.
"The highlight of Exercise Saber Strike 2022 in Lithuania is a combined operation to take place next week: troops of Kestutis Motorized Infantry Battalion will be deployed from Pabrade to Kazlu Ruda Training Area by US, UK and Lithuanian aircraft and conduct combat actions according to the exercise scenario."