Correspondents for RIA and TASS both reported the incident based on what they saw from the minister's plane. They said the NATO jet was "driven off" by a Russian Su-27 fighter, which "demonstrated" its armament by swinging its wings.

A NATO official confirmed that three Russian aircraft, including two fighters, were tracked over the Baltic Sea Wednesday.

"As the aircraft did not identify themselves or respond to air traffic control, NATO fighter jets scrambled to identify them, according to standard procedures. NATO has no information as to who was on board. We assess the Russian pilots' behaviour as safe and professional," the official said.

The same NATO official added that all sides involved acted in a safe and professional manner,

When asked by CNN if the NATO jet was chased away, the official said: "Once identification of the aircraft was complete, our jets broke away as it is standard procedure."

The Russian Defense Ministry has not responded to requests for comment from CNN. A television network run by the ministry released a video online that it described as showing the incident.

Shoigu was on his way to the Russian enclave of Kaliningrad, which is between Moscow and Poland.

Russian state media also reported that a NATO jet shadowed Shoigu's plane when he departed Kalingrad, but did not approach as closely as in the prior incident.

Wednesday's encounter with a NATO jet comes just two days after a Russian Su-27 fighter jet flew within five feet of a US Air Force RC-135 reconnaissance aircraft in the skies above the Baltic Sea.

US officials deemed that intercept "unsafe" as the armed Russian jet flew "erratically," in close proximity to the American spy plane.

Russia disputed claims that its aircraft was at fault during the encounter and said it intercepted two US reconnaissance aircraft as they "approached the Russian state border."

There have been more than 30 interactions between Russian and US aircraft and ships near the Baltic Sea since the beginning of June, a US official told CNN. The vast majority of these encounters have been safe and professional, the official added -- a point that adds to the significance of Monday's incident.

"Russia is certainly within its right to exercise within international airspace, but we want them to respect international standards for safety to prevent accidents," said Pentagon spokesperson Capt. Jeff Davis.

"The vast majority of interactions we have, intercepts that occur when we fly and that are intercepted by the Russians are safe. This is an exception, not the norm, but we were again operating in international airspace and did nothing to provoke," Davis said.

These recent intercepts occurred amid rising tensions between Russia and members of NATO -- particularly the US.

Earlier this month, the US Air Force deployed long-range B-52 bombers and 800 airmen to the United Kingdom in support of joint exercises with NATO allies and partners across Europe.

Those exercises have primarily taken place in the Baltic Sea, the Arctic and along Russia's border with several NATO partners.

Over the weekend over 1,000 US and NATO troops conducted a defensive drill in the Suwalki Gap in the border area between Poland and Lithuania. That area is seen by most experts as a likely Russian target in the event of a NATO-Russia military confrontation.

CNN's Oksana Brown, Mary Ilyushina, Pamela Boykoff, Emma Burrows and Ryan Browne contributed to this report.

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NATO jet intercepts Russian minister's plane - CNN