Two Russian intelligence gathering ships are currently shadowing U.S. Navy and other NATO vessels operating in the Baltic Sea during a major international exercise this month, according to U.S. Navy Vice Admiral James G. Foggo III, leading the exercise.

“What we have seen is shadowing by two Russian intelligence vessels since we left port in Tallinn, Estonia” on June 5th, Foggo said. He added that the Russian ships have been “well behaved” but have refused to communicate with the U.S. Navy despite coming as close as one mile at times with U.S. and allied vessels.

Foggo also commands the U.S. Navy’s 6th Fleet, responsible for the waters around Europe, and spoke to reporters on a conference call Wednesday while on his command ship, USS Mount Whitney, currently steaming off the coast of Poland.

The exercise, BALTOPS 2016, is in its 44th year and includes more than 40 ships from 17 nations and some 6,000 sailors, airmen and marines conducting training operations from June 3-19. Non-NATO counties Finland and Sweden are also participating.

According to other NATO officers on the conference call, Russia normally likes to take a peek at the exercise, but tensions were heightened this year as NATO announced plans to deploy troops to Eastern Europe to deter Russian aggression in the region, which Russia says violates longstanding treaties between Russia and the West.

Russia’s annual uninvited participation in the large Baltic naval exercise comes with “less intensity” this year compared to 2015, according to Foggo, but what concerns him is Russia’s recent announcement to conduct its own large-scale exercise in the near future without sharing any of the details. Western forces are typically more open with Russia about their own exercises.

Last week, a delegation from the U.S. Navy met its Russian counterparts in Moscow to discuss the current Baltic Sea exercise, and had “candid and frank discussions about how to operate professionally [and] not get in each other’s way,” Foggo said, calling the meeting “productive.”

He added, “We didn’t want any surprises. We actually put our schedule for the exercise on the web.” But the Russians have not returned the favor, according to Foggo.

“Frankly, it would be nice to see some of that transparency on the Russian’s part.”

Foggo said the Russians have a habit of conducting sudden large-scale surprise or “snap” exercises in the region “that can make people nervous.”

Russia announced this week it would be launching one of these “snap” exercises soon.

“We’re wondering where that’s going to be,” Foggo said, adding that he’d seen reports on Russia’s announcement of a “big” exercise in the coming days.

Previous large-scale Russian exercises have turned into invasions. In 2014, Russia invaded Ukraine and annexed Crimea under the guise of a sudden “snap” military exercise.

In addition to the large multi-national naval exercise in the Baltics, the U.S. Army and NATO allies are conducting the largest exercise in Poland since the end of the Cold War involving some 30,000 troops from 24 different countries. Foggo said he did not know which exercise was drawing Russia’s ire.

According to Foggo, Russian activity this time around the Baltic exercise is “certainly, nothing like we saw with the close fly-by of USS Donald Cook [in April] right here in the Baltic Sea.”

Foggo thought the media attention brought against Russia when its warplanes buzzed the U.S. Navy destroyer in April in the Baltic Sea might have made Russia change course.

“I don’t think they want to be seen that way,” said Foggo. “That might have caused the change in their behavior.”

When asked if the buzzing of the USS Donald Cook by Russian warplanes in April came up during the meeting between U.S. Navy and Russian officials last week in Moscow, Foggo said “that type of interaction was discussed” but declined to disclose any specifics.

The vice admiral said he has seen “a little” Russian air activity operating near his ships.

Foggo said he saw for the first time with his own eyes a Russian Su-24 strike aircraft Tuesday night fly over his command ship and a Royal Navy helicopter carrier nearby. That would have been the same type of Russian jet that buzzed the Navy destroyer in April.

“They stayed at altitude and conducted a standard reconnaissance of an at sea flotilla,” Foggo said, adding that the Russians operated in a “safe and professional” manner. He said a Ka-27 “Helix” helicopter was also spotted Wednesday morning near allied vessels.

“I personally think the Russians have changed their calculus,” since April, Foggo claimed. He said Russia was still finding other ways to protest the large Baltic exercise.

“The operations on Finnish soil were greeted with disdain by the Russian Foreign Minister Lavrov,” according to Foggo. He said Finland’s foreign minister had been meeting with Lavrov in Moscow during an amphibious landing in Hanko, Finland, the first of three landings taking place this month.

U.S. Air Force B-52 bombers also have taken part in the Baltic exercise to launch “quick strike mines” and give other allied ships the opportunity to practice mine clearance operations, which has uncovered some unexploded mines and torpedoes dating back to the World War II era. “It was real world training,” said Foggo.

The vice admiral said he had not seen any signs of Russian submarines operating near his forces, but warned in a recent article that the technology gap between Russia and the U.S. was closing fast.

“These are not the [Russian] submarines we faced during the Cold War,” Foggo said in a recent article in the U.S. Navy Institute’s Proceedings Magazine.

“There may be fewer of them, but they are much stealthier, carry more devastating weaponry, and go on more frequent and longer deployments than before. The submarines of the Russian Federation are one of the most difficult threats the United States has faced. This threat is significant, and it is only growing in complexity and capacity,” he said.

Russian submarine deployments are up 50% in the past few years according to a recent report quoting the former head of the Russian Navy.

Foggo said there is particular concern in the Black Sea where Russia is adding four more Kilo-class submarines to the two already in place. A similar Kilo-class submarine entered the Mediterranean and launched a Kalibr cruise missile into Syria, another concern about the growing Russian military threat in the region.

“We need to remain vigilant,” Foggo said.

The presence of Russian military forces this month around the large multi-national naval exercise in the Baltics is not new according to NATO officials who say they've seen Russians trailing allied vessels for decades.

“When I was a junior officer on a submarine in 1983, the Russian AGI [intelligence ship] used to wait for us when we came out of Charleston, South Carolina and they were right at the limit of our territorial waters,” said Faggo.

Lucas Tomlinson is the Pentagon and State Department producer for Fox News Channel. You can follow him on Twitter: @LucasFoxNews