The Russia-Belarus exercises, running until February 20, have provided Moscow with cover to further increase forces near Ukraine at a time when the United States and Britain have warned that Moscow may be gearing up for war.
Ukraine's defence minister said Russia had currently massed a total of 115,000 troops near Ukraine's borders.
Russia denies planning to invade Ukraine and has described the Allied Resolve exercises with Belarus as a rehearsal in repelling external aggression.
It has not disclosed the size of its forces there but says they will withdraw after the drills.
NATO Secretary-General Jens Stoltenberg said there has been significant movement of Russian military forces into Belarus over the last few days.
"This is the biggest Russian deployment there since the Cold War, with an expected 30,000 combat troops," he said.
The Russian deployment included Spetsnaz special operations forces, SU-35 fighter jets, S-400 air defence systems and nuclear-capable Iskander missiles.
Russian Defence Minister Sergei Shoigu arrived in Belarus on Thursday to inspect Russian and Belarusian troops and was due to meet Belarusian leader Alexander Lukashenko, Interfax news agency said.
The United States and NATO have rejected Russian demands to bar Ukraine from joining NATO and withdraw allied forces and weapons systems from eastern Europe, while expressing a willingness to talk about arms control and confidence-building measures.
Russian President Vladimir Putin said on Tuesday the West had ignored Russia's main concerns and accused the United States of trying to lure it into war, but he said Russia was still interested in dialogue.
On Thursday the Kremlin again accused Washington of inflaming tensions after the United States said it would send nearly 3000 extra troops to Poland and Romania.
The Pentagon said the aim was to send a "strong signal" to Putin and the world that "NATO matters to the United States and it matters to our allies".
Turkish President Tayyip Erdogan, who has offered to mediate between Russia and Ukraine in the crisis, was due to visit Kyiv on Thursday.
Ukraine and Turkey will sign a framework agreement on manufacturing Turkish drones in Ukraine, Defence Minister Oleksii Reznikov told reporters, in a move that is certain to annoy Moscow.
Ukraine has already deployed Turkish-made drones in a war with Russian-backed separatists in the east of the country.
