Nils Muiznieks, the council's commissioner for human rights, said Monday that countries such as Greece and Hungary that have seen members of extremist political parties elected to their parliaments are obligated by treaty to pass and impose laws curbing their influence.
"It worries me deeply that the European community and national political leaders appear not to be fully aware of the serious threat that these organizations pose to the rule of law and human rights," he said.
Muiznieks, in charge of evaluating the human rights situations among the 47 members of the Council of Europe, said the increasing popularity of such parties as Golden Dawn in Greece and Jobbik in Hungary is abetting an upsurge of racist attacks and violence throughout the continent.
For instance, 220 racist attacks were reported in Greece from October 2011 and December 2012, "about one attack every other day," he noted.
The upsurge has reached the point of "an early form of far-right terror," he said.
"The phenomenon is all the more serious as it is paired with an increased influence of racist extremist political parties in national parliaments and governments, and endeavors by these parties to strengthen their position at European level through alliances," he said.
In Hungary, he noted, Jobbik -- a self-described as "radically patriotic" party -- emerged as a political force in 2010 and quickly became the country's third-largest party, while the "neo-Nazi" Golden Dawn and Sweden Democrats have also marked political gains.
Muiznieks reminded European countries they are obligated under the United Nations' 1966 International Convention on the Elimination of All Forms of Racial Discrimination to eliminate racial discrimination as well as outlaw hate speech and criminalize membership in racist organizations.
He urged governments to update and strengthen their anti-racism laws and to engage in "systematic, continuous anti-racism training" of police, prosecutors and to counter what he called their "low awareness" of the threat posed by racist crimes.
The call came less than a month after Muiznieks issued a report on Greece, in which he said an outright ban on Golden Dawn would be "possible" as lawmakers consider a bill pending since 2011 that would introduce tougher sentences for racially motivated crime and prevent MPs who advocate neo-Nazism from running for office.
Police have alleged Golden Dawn MPs were involved in several cases of racist and violent attacks against immigrants last year.
The Greek anti-racism bill was to be put before Parliament by justice ministers last week but was delayed due to disagreements among governing coalition members, Kathimerini reported.
The newspaper, citing government sources, said the dispute appeared to center on whether it is the best way to counter Golden Dawn, with some contending it would only make the group more popular by casting it in the role of a victim of oppression.
The government, meanwhile, contends it is already battling racist extremism, establishing an anti-racism prosecutor in Athens as setting up 70 anti-racist police units, the EUobserver reported.
In a response to Muiznieks' report, it cautioned that taking measures against groups such as Golden Dawn that have legally been elected to Parliament is "complex" for "obvious reasons related to the function of democratic polity."