NAPLES, Italy — Russian attack submarines, the most in two decades, are prowling the coastlines of Scandinavia and Scotland, the Mediterranean Sea and the North Atlantic in what Western military officials say is a significantly increased presence aimed at contesting American and NATO undersea dominance.

Adm. Mark Ferguson, the United States Navy’s top commander in Europe, said last fall that the intensity of Russian submarine patrols had risen by almost 50 percent over the past year, citing public remarks by the Russian Navy chief, Adm. Viktor Chirkov. Analysts say that tempo has not changed since then.

The patrols are the most visible sign of a renewed interest in submarine warfare by President Vladimir V. Putin, whose government has spent billions of dollars for new classes of diesel and nuclear-powered attack submarines that are quieter, better armed and operated by more proficient crews than in the past.

The tensions are part of an expanding rivalry and military buildup, with echoes of the Cold War, between the United States and Russia. Moscow is projecting force not only in the North Atlantic but also in Syria and Ukraine and building up its nuclear arsenal and cyberwarfare capacities in what American military officials say is an attempt to prove its relevance after years of economic decline and retrenchment.