MADRID — The leader of Spain’s far-right Vox party, Santiago Abascal, made his name as an opponent of separatism in his home Basque region. But it is the secessionist conflict in Catalonia that has provided his real opportunity.

As the Catalan turmoil confronts Spain with an existential crisis that threatens its territorial integrity, Mr. Abascal, who prides himself on owning a Smith & Wesson handgun, has presented himself as the fiercest defender of Spanish sovereignty.

That appeal has tapped into a new nationalism in Spain. Over the last 11 months, his party has gone from a non-factor to being the country’s third most powerful political force, as Vox doubled its representation to 52 seats in the 350-seat Parliament in elections on Sunday.

The election results have left Spain looking at more uncertainty and deadlock. Pedro Sánchez, the caretaker Socialist prime minister, now faces another round of complicated negotiations to form a government.