Washington (CNN) "Good morning, American pilots. We are here to greet you on your Fourth of July Independence Day."

That was the message two Russian bombers delivered while flying within tens of miles of the California coast this month to the U.S. fighter jets that intercepted them, according to the North American Aerospace Defense Command.

The greeting may have been unusual, but the close encounter was not. Russian military planes have been encountered near U.S. airspace a number of times before.

On June 4, 2014, U.S. fighter jets intercepted Russian bombers off Alaska and California following a string of aerial encounters over the Pacific.

According to U.S. defense officials, four long-range Russian Tu-95 Bear-H bombers, accompanied by an aerial refueling tanker, flew into the U.S. Air Defense Identification Zone, an area extending 200 miles from the North American coast, off Alaska, where they were intercepted by U.S. F-22 fighter jets.

Two of the Russian bombers peeled off and headed west, while the other two flew south and were identified by U.S. F-15 fighters within 50 miles of the California coast.

Capt. Jeff Davis, a spokesman for the North American Aerospace Defense Command, said at the time that it was the first time American jets had intercepted Russian military aircraft off California since 2012 -- an encounter that also took place on July Fourth.

Davis said the Russian planes were entirely within their rights, and it was a professional encounter on both sides. He said in 2014 that Russian flights into the air defense zone are intercepted about 10 times a year.

Increased military activity

Close encounters between Western countries and military vessels from other countries are not limited to the U.S. Nor are they limited to the air.

In November 2014, a foreign submarine -- unlike the Russian planes off the U.S. coast -- actually trespassed in Swedish territory, officials there said. But they couldn't say what country the vessel belonged to.

The Swedish newspaper Svenska Dagbladet reported that the military became suspicious after Swedish intelligence picked up an emergency radio call in Russian. But Russia denied that it had any vessel in Swedish waters.

In general, Russian military activity has increased since March 2014, when Western countries objected to its annexation of the Ukrainian peninsula of Crimea as well as to Russia's alleged support for separatists in eastern Ukraine.

In May, for example, Russia annoyed Western officials by deploying 12,000 troops and numerous aircraft and weapons in a surprise military exercise in the country's northwest -- a show of strength that appeared to be a response to a long-planned -- and long-announced -- European military exercise led by Norway.

And in June, Russian President Vladimir Putin announced the addition of 40 intercontinental ballistic missiles to Russia's nuclear arsenal.

The July 4 aerial encounter this year, between Russian Tu-95 "Bear" bombers and American F-15s, came on the same day that Russian President Vladimir Putin sent best wishes to President Barack Obama for the July Fourth holiday.

The Russian pilots used an emergency aircraft communication channel to send the message, a NORAD spokesman told CNN on Wednesday, providing new details about an event first reported earlier this month.

He declined to describe the move as a threat but said the incident was "potentially destabilizing," because the Russian approach was unannounced and the bombers in question are nuclear-capable.

Bombers didn't enter U.S. airspace

American fighters also intercepted two other Russian Tu-95 bombers on July Fourth, off the southern coast of Alaska, according to the U.S. military.

In neither case did the Russian planes enter U.S. airspace, which extends 12 nautical miles from American coastlines, officials said. The U.S. fighters tracked them until they turned around.

Photos: Russian warplane intercepts Photos: Russian warplane intercepts A Russian Tu-95 Bear bomber is escorted by a British Royal Air Force Typhoon fighter during an intercept in September 2014. Click through the gallery to see other intercepts in late 2014. Hide Caption 1 of 12 Photos: Russian warplane intercepts NATO Secretary General Jens Stoltenberg said in November that alliance fighters had intercepted Russian warplanes as they flew close to NATO countries more than 400 times in 2014, the kind of Russian air activity not seen since the Cold War. Hide Caption 2 of 12 Photos: Russian warplane intercepts An armed MiG-31 intercepted by Norwegian planes. The plane is nicknamed the Foxhound by NATO. Hide Caption 3 of 12 Photos: Russian warplane intercepts An armed Tu-22M supersonic bomber, nicknamed the Backfire by NATO, was photographed by Norwegian fighter jets. Hide Caption 4 of 12 Photos: Russian warplane intercepts A look at a Russian Tu-22M from below as taken by a Norwegian Royal Air Force fighter plane. Hide Caption 5 of 12 Photos: Russian warplane intercepts A Su-24 attack aircraft, nicknamed the Fencer by NATO, was photographed by a Norwegian warplane. Hide Caption 6 of 12 Photos: Russian warplane intercepts An armed MiG-31 Foxhound photographed from below by a Norwegian Royal Air Force interceptor. Hide Caption 7 of 12 Photos: Russian warplane intercepts A Russian Il-78 tanker refuels a Tu-95 Bear bomber in a photograph taken by a Norwegian warplane. Hide Caption 8 of 12 Photos: Russian warplane intercepts Two Russian Sukhoi Su-34 fighter bombers, nicknamed the Fullback by NATO, as photographed by Finnish Air Force F/A-18 Hornet fighters. Hide Caption 9 of 12 Photos: Russian warplane intercepts Finnish fighter jets photographed this Russian Tu-95 Bear bomber. Hide Caption 10 of 12 Photos: Russian warplane intercepts Two Tupolev Tu-22M aircraft intercepted by Finnish fighter planes. Hide Caption 11 of 12 Photos: Russian warplane intercepts A Russian Tupolev Tu-95 Bear bomber intercepted by Finnish fighter planes. Hide Caption 12 of 12

The bombers off California flew roughly 40 miles from the state's central coast, the NORAD spokesman said.

That encounter was more unusual as Russian planes don't often venture that far south, a U.S. military official told CNN a few days afterward . Russia conducted a similar flight off the West Coast on July Fourth in 2012.

While the intercepts were routine from a military point of view, the U.S. official said, the Pentagon sees them as Putin "sending a message" to the United States on Independence Day.

Putin's official message

In his official message to Obama, Putin expressed confidence that Moscow and Washington could "find solutions" to international issues.

He said that despite differences between the two countries, "Russian-American relations remain the most important factor of international stability and security," according to a Kremlin statement.