The exercise, involving US and NATO vessels, includes more than 40 ships and some 6,000 sailors, airmen and marines conducting training operations from June 3-19.
Non-NATO counties Finland and Sweden are also participating.
Foggo, who is the commander of US 6th Fleet, said Russian forces had been “well behaved and professional on the high seas as we conducted our exercises.”
Foggo said a delegation from the USNavy met its Russian counterparts in Moscow last week to discuss the current maritime exercise.
They had “candid and frank discussions about how to operate professionally [and] not get in each other’s way,” he said, calling the meeting “productive.”
Foggo said the Russians had a habit of conducting sudden large-scale surprise or “snap” exercises in the region “that can make people nervous.”
Russia announced this week that it would be launching one of its “snap” exercises in the near future without sharing any of the details.
The NATO exercise comes amid continued strain in relations between Russia and NATO, which have been at odds since Crimea seceded from Ukraine and joined the Russian Federation following a referendum in March 2014.
NATO ended all practical cooperation with Russia in April that year over the ensuing crisis in Ukraine.
The West accuses Moscow of supporting pro-Russian forces in the Ukrainian conflict but Russia denies the allegation.
Tensions, billed by some as a resurgent Cold War, have seen NATO resorting to military buildup in Russia’s backyard and the latter staging military maneuvers and flying aircraft close to US destroyers in the Baltic Sea.