The owners of the 12-metre sailboat Bright Future say the shots were fired on Tuesday morning when they encountered a Russian warship while crossing the English Channel to Cherbourg in France.
Russia says the crew of the frigate Admiral Grigorovich fired shots into the air after the sailboat failed to respond to warnings to change course.
No one was injured but the incident underscored heightened tensions between the UK and Russia.
Speaking at the G7 summit in France, Starmer said the incident was "deeply concerning", even though British defence officials have concluded the shots were not "anything more sinister" than an effort to avoid a collision.
"That doesn't take away from the fact that clearly Russia is aggressive across Europe," Starmer said on Wednesday.
The incident occurred two days after Britain seized a tanker from Russia's so-called shadow fleet, which Western powers say is used to skirt sanctions on Russian oil exports imposed after the invasion of Ukraine.
Britain has also accused Russia of mounting a campaign of sabotage and misinformation designed to destabilise European nations that support Ukraine.
The British couple aboard the Bright Future, Jane Kelvey, 68, and her husband Alan, 70, reported that the shots were fired about 40km south of the Isle of Wight, outside UK territorial waters.
"It was a bit scary," Jane Kelvey told the i Paper.
"I crouched down. I didn't think our safety was in danger. But it was certainly unusual. As we sailed away, we said to each other, what the hell just happened?"
Russia's defence ministry said the crew of the frigate tried to contact the yacht when it was seen sailing on a "dangerous course in close proximity with the warship".
It said the ship's crew launched flares and issued sound signals when the yacht did not respond.
"After the distance had closed to 150m, the frigate's commander decided to fire warning shots across the vessel's bow using small arms," the ministry said.
It said the yacht then changed course and sailed away.
with Reuters
