BUDAPEST, Hungary — As Europe marks the 100th anniversary of the outbreak of World War I, the war that destroyed Old Europe, far-right parties are gaining ground across New Europe.

Most of the far-right parties are pro-Russia, opposing U.S. and European Union efforts to isolate President Vladimir Putin for his intervention in Ukraine. They are expected to do well in the May 25 European Parliament elections.

Last month, I traveled to Hungary and Greece, where the neo-fascist movements are strongest. In Hungary, the extreme-right Jobbik party won 1 in 5 votes in last month’s parliamentary election. In Greece, even as the neo-Nazi Golden Dawn party is being prosecuted by the government as a criminal organization, it remains the fourth-largest political party in the country. Golden Dawn lawmaker Ilias Kasidiaris, who sports a swastika tattoo and once read from “The Protocols of the Elders of Zion” on the floor of Parliament, is running for mayor of Athens.

Both parties deny being inherently anti-Semitic or anti-Roma, but their symbols and rhetoric suggest otherwise. Party leaders are unapologetically hostile to LGBT rights, and Golden Dawn is vehemently anti-immigrant. And in both Greece and Hungary, many voters appear to be either overlooking the neo-fascist message or embracing it.

Despite international condemnation of Jobbik’s anti-Semitic, anti-Roma vitriol, support for the party rose from 18 percent in the 2010 elections to 21 percent last month. Among those re-elected to office was a Jobbik member of parliament who demanded that the government draw up a list of Jews in official positions because they posed a “national security risk.” Another winning candidate claimed that “the Gypsy people are a biological weapon” of the Israelis who have “occupied” Hungary. These are not idle words in a country where Roma have been terrorized or killed in organized attacks.

The Hungarian media have reported that Jobbik is toning down its rhetoric to appeal to a wider range of voters. But covert anti-Semitic messages still hide in plain sight. One Jobbik advertisement shows a wholesome family eating at a dinner table in front of a bookshelf filled with works by notoriously anti-Semitic writers. I heard Jobbik candidates on the stump in a working-class neighborhood of Budapest complaining about “international bankers” and griping about how telling “a Jewish joke” was the worst crime a Hungarian politician could commit nowadays.

In Greece, the government is locked in a remarkably belated battle with Golden Dawn. In 2010, the party was on the margins, winning only 0.2 percent of the vote. But then, as the economy collapsed, gangs of neo-Nazi thugs began terrorizing migrants, including traumatized Syrian refugees, and support for Golden Dawn surged. In 2012, the party claimed 7 percent of the vote and 17 seats in Parliament, a victory Golden Dawn leaders reportedly took as approval for “protecting” Greeks from a flood of immigrants.

A migrant worker from Africa was attacked by thugs who carved Golden Dawn’s insignia into his back, an Egyptian was tortured, and a Pakistani was killed bicycling to work. Human rights groups counted at least 320 victims of racist violence in Greece last year alone. But it was not until September’s slaying of a Greek citizen, the anti-fascist rap musician Pavlos Fyssas, that the government moved against Golden Dawn, arresting most of its senior leadership and alleging that it is a criminal organization engaged in offenses ranging from weapons possession to murder.

The party’s “Fuhrer” and several others remain in jail, while two special magistrates investigate. Yet a defiant Golden Dawn is still advancing candidates for both local and European Parliament elections this month, and some of its alumni say they will stand under a new name, National Dawn.

In Greece and Hungary, the far right is clearly growing in popularity. The question now becomes the degree to which voters in these countries and across Europe are becoming accustomed to the rhetoric of the neo-fascist movements, and the extent to which the ruling parties pander to right-wing voters.

Oddly, the best hope for a democratic Europe may lie in the traditional disdain of Western European right-wingers for Eastern and Southern Europeans, and squabbling within the far right over which of the national parties are so extreme as to cause an image problem. These internal tensions could prevent the European neo-fascists from forming a functional continental alliance — just as in Old Europe.

Sonni Efron, a former State Department official and a former Los Angeles Times reporter, is a senior fellow at Human Rights First. He wrote this column for the Los Angeles Times.