"We don't want to be disappointed in our [U.S.] colleagues again, and therefore we are assuming the worst-case scenario in our military planning," Russia's deputy foreign minister said.
"I don't think the French expect me to respond to tweets," the country's president said.
Russian Prime Minister Dmitry Medvedev called NATO's 2011 intervention in Libya "a cynical deception" and said Moscow was "ready to cooperate" on peace initiatives.
The German chancellor's support of French President Emmanuel Macron's calls for a unified European force came as U.S. President Donald Trump criticized the idea, mocking France's loss to the Nazis in World War II.
"Russia is known to possess such capabilities," said Finnish Prime Minister Juha Sipila.
"For over five years, the United States has pursued diplomatic and technical avenues with Russia aimed at preserving the INF Treaty," NATO Secretary-General Jens Stoltenberg said.
Around 50,000 troops, 65 vessels, 150 aircraft and 10,000 vehicles will take part in Trident Juncture 2018.
All of NATO's 29 members will take part in the exercises, as will the alliance's partners Sweden and Finland.
U.S. Navy Admiral James Foggo said one of the exercise's messages was to "show NATO is capable of defending, it is capable of deterring any adversary."
"It is time now for Russia to come to the table and stop the violations," the U.S. ambassador to NATO told reporters.
The bombers were "a hazard to all other aviation," the Ministry of Defence said.
The exercises are taking place as tensions rise between Russia and Ukraine in the Sea of Azov.
The drill involves all branches of the military, as well as deployments from China and Mongolia.
Russia's foreign minister gave his thoughts on the odds of an armed clash and said Russian meddling claims show Washington does not "respect the American choice at all."
Russia will mobilize up to 300,000 troops, more than 1,000 aircraft, around 80 warships and some 36,000 vehicles.
Russian media have worked to promote tensions between Turkey and NATO, encouraged Ankara to support Russian actions in Eurasia and the Middle East and influenced the country's internal political development to transform it into a "more compliant partner."
Given President Donald Trump's animosity toward both John McCain and NATO, such a move could be seen as a challenge to the White House.
The Air Force is pre-positioning the deployable air base system throughout Europe, so they can be pushed out rapidly in the face of any threat.