BRUSSELS — British ships and a helicopter were dispatched over the Christmas holiday weekend to track an “upsurge” of Russian naval vessels passing near British waters, the British Navy said Tuesday, as British and NATO leaders warn of Russian naval activity at levels unseen since the Cold War.

At least four Russian ships, including a warship and an intelligence-gathering ship, passed near British waters starting on Saturday, the British Navy said. The traffic on the water meant British sailors on the Royal Navy frigate St. Albans spent Christmas tracking their Russian counterparts.

The ship traffic came days after the head of the British military warned in an interview of the threat of Russian submarine activity near the sensitive undersea data cables that carry internet traffic between North America and Europe.

“I will not hesitate in defending our waters or tolerate any form of aggression,” said British Defense Secretary Gavin Williamson in a statement. “Britain will never be intimidated when it comes to protecting our country, our people, and our national interests.”

Russian ships routinely sail through international waters near British territory as they pass from ports in northern Russia into the open Atlantic or into the Mediterranean, where they have been involved in Russia’s intervention in Syria. Before formally entering Russian naval service, ships are often tested in the international waters of the North Sea.

The British Navy did not allege any misbehavior or territorial violations, and because it does not routinely publicize its encounters with Russian ships, it was not clear how unusual the Christmas movements were.

The navy said that a Russian warship, the Admiral Gorshkov, passed close to British territorial waters Saturday and that the St. Albans frigate was dispatched to escort it as it passed through the North Sea. It released several grainy photographs of the two ships sailing closely to each other in what appeared to be choppy waters.

The Russian ship is still undergoing testing and has not yet formally entered into service, according to its shipbuilder.

Because the Admiral Gorshkov is still in sea trials, it probably does not yet pose a military threat, said Michael Kofman, an expert on the Russian military at the Center for Naval Analyses.

The Gorshkov is the long-awaited flagship of a new class of stealth missile frigate. Originally scheduled to enter service in 2013, shipbuilders said Monday it was still undergoing tests 11 years after construction started.