"A nation which introduces the death penalty has no place in the European Union," Juncker told the German daily newspaper Suddeutsche Zeitung in an interview on Monday.
"It's grounds for divorce."
"Hungary will stop at nothing when it comes to protecting its citizens," said Orban.
Following his comments, Juncker asked Orban to "immediately make clear that this is not his intention [to reintroduce the death penalty]."
"If it would be his intention it would be a fight," said Juncker," noting that the EU's charter of fundamental rights "forbids the death penalty."
Chapter One, Article Two of the charter states that "No one shall be condemned to the death penalty, or executed."
"The European Union has a strong and unequivocal opposition to the death penalty in all times and in all circumstances," wrote the EU Council in guidelines it released on the death penalty in 2013.
Juncker and Orban appear not to take their political differences personally; at the EU summit which was held in Riga in May Juncker set the stage for Orban's arrival by joking "the dictator is coming," before greeting Orban with a friendly handshake and the word "dictator."
The EU chief executive gave the Hungarian leader a playful slap, who responded with a smile and some jostling on the stage.
Hungary, which became an EU member in 2004, abolished the death penalty in November 1990.
