Mr Griffin was invited to the two East European countries by representatives of extremist parties who had made trips to Britain earlier in the year.
A fragile pan-European Parliament alliance last year collapsed in disarray after five Romanian nationalists walked out, claiming they had been insulted by their Italian colleagues. The effect of the walk-out was to put the group below the minimum number of seats required to allow it to participate in the parliament.
Now Mr Griffin is planning another attempt to bring together extremists - the BNP calls them "nationalists" - from Belgium, Austria and Italy, as well as the Czech Republic and Hungary. After a first stop in Budapest, he will be heading to Prague for Czech National Day on October 28. Earlier this year, a Czech right-winger spoke at the BNP's Red, White and Blue Festival.
Gerry Gable, the veteran anti-fascist and publisher of Searchlight magazine, said: "They are clearly hoping they will be able to pick up the extra seats they need. However, they may not be successful because the European Parliament has increased slightly the number of seats necessary.
"In the past year, Griffin has associated himself with a number of very hard-line extremists. In May, members of an extreme group from Hungary came here and a member of the Czech Republic was here several weeks ago to talk to the Greenwich and Bexley branches of the BNP. Only a few days ago, a number of people were sprayed with acid in an antisemitic attack in Hungary.
"I know Griffin has made overtures to the community in the past couple of years to try to shed the BNP's image of being antisemitic, and has been firmly rebuffed. But when he is consorting with these people in Europe, it rather gives the lie to what he says he trying to do."
Winston Pickett, director of the newly formed European Institute for the Study of Contemporary Antisemitism, said: "Griffin's tour has come against a backdrop of renewed and increased political activities by the Hungarian far-right.
"In particular, the Jobbik party [Movement For a Better Hungary] wants to forge alliances with other right-wing groups in order to create a united front ahead of the European elections next June."
Simon Darby, the party's deputy leader, confirming the invitations, said the BNP was following only what other groups had done in Europe in trying to form a "nationalist bloc".