US-led NATO drills began Monday in the Baltic states and Poland, a move intended to reassure Russia's nervous neighbours amid tensions over Ukraine.

Russia's increased military presence in the Baltic Sea and regional airspace since its annexation of Crimea from Ukraine last year has jangled nerves in the area, which lay behind the Iron Curtain 25 years ago.

More than 6,000 troops from 13 NATO countries are participating in the Saber Strike 2015 drills in Estonia, Latvia, Lithuania and Poland, all EU and NATO members.

"This is one of the biggest exercises in Lithuania since we joined NATO" in 2004, Major General Almantas Leika, commander of Lithuania's land forces, told reporters in Vilnius.

"The huge allied presence demonstrates solidarity with the countries of this region," he said, adding that Lithuania is hosting the command centre for the drills.

NATO has been guarding the skies over the three small Baltic states since 2004, when they joined the defence alliance but lacked the air power to monitor their own airspace.

Last month, the Baltic trio formally asked NATO to permanently deploy several thousand troops in their region as a deterrent to Russia.

NATO has not yet replied to the request, military spokesman Lithuanian Captain Mindaugas Neimontas told AFP.

The exercises, organised by the US Army in Europe, will run until June 19 and include Abrams tanks and B-52 bombers, General Leika said.

The drills take place after Russia last week began conducting unexpected war games involving 12,000 troops and 250 aircraft, at the same time as NATO planes joined Nordic air forces for a drill in Sweden's sub-Arctic north.