Mr Meuthen compared the AfD to the League party led by Matteo Salvini, which has quickly established itself as a national movement in Italy after beginning as a regional party in the north.
“We are going in that direction, except that here change is coming not from the north of the country but from the east,” he said.
The AfD opposes migration to Germany and has been associated with anti-Muslim campaigns, but its connection to right-wing extremism means it presents a great threat is to Jews, one German Jewish community leader said.
Josef Schuster said he was relieved that the worst case scenario — a big AfD victory — had been avoided.
But JTA quoted him as saying it would be “devastating to sit back and relax” just because the right-wing party did not gain first place.
Andreas Kalbitz, the AfD leader in Brandenburg, hailed his party’s performance and said it showed “we are here to stay”.
Mr Kalbitz was mired in controversy in the week before the election after it emerged he had attended a neo-Nazi rally in Athens 12 years ago.
His name appeared in a police report as one of 14 German citizens who attended the rally for the Patriotic Alliance, a short-lived movement formed by members of Golden Dawn.
The report, which was published by Der Spiegel, said the delegation that accompanied Mr Kalbitz draped a swastika flag over a balcony. The AfD Brandenburg leader denied he was linked to that incident and said he attended the rally out of “curiosity”.