Some of Russia’s European fans, particularly those with a religious bent, are attracted by Mr. Putin’s image as a muscular foe of homosexuality and decadent Western ways. Others, like Aymeric Chauprade, a foreign policy adviser to the National Front’s leader, Marine Le Pen, are motivated more by geopolitical calculations that emphasize Russia’s role as a counterweight to American power.

Russia has added to its allure through the financing, mostly with corporate money, of media, research groups and other European organizations that promote Moscow’s take on the world. The United States also supports foreign groups that agree with it, but Russia’s boosters in Europe, unlike its leftist fans during the Cold War, now mostly veer to the far right and sometimes even fascism, the cause Moscow claims to be fighting in Ukraine.

Hungary’s Jobbik, one of Europe’s most extreme nationalist parties and a noisy cheerleader for Moscow, is now under investigation by the Hungarian authorities amid allegations that it has received funding from Russia and, in a case involving one of its leading candidates for the European Parliament, that it has worked for Russian intelligence.

No longer dismissed, as they were for decades, as fringe cranks steeped in anti-Semitism and other noxious beliefs from Europe’s fascist past, the National Front and like-minded counterparts elsewhere on the Continent are expected to post strong gains in this week’s election, which begins on Thursday in Britain and the Netherlands and then rolls across Europe through Sunday.

But they are unlikely to form a cohesive bloc: Nationalists from different countries tend to squabble, not cooperate.

Nigel Farage, the leader of the United Kingdom Independence Party, a group zealously opposed to the European Union and a critic of American foreign policy, is already engaged in a bitter feud with Ms. Le Pen.

But Mr. Farage and Ms. Le Pen have at least found some common ground on Russia. The British politician recently named Mr. Putin as the world leader he most admired “as an operator but not as a human being,” he told a British magazine.