TBILISI, Georgia — Mikheil Kavelashvili, a hardline critic of the West, was sworn in as president of Georgia on Sunday amid a political crisis after the government froze European Union application talks in a move that sparked major protests.

Outgoing President Salome Zourabichvili, a pro-EU opponent of the ruling party, said in a defiant speech to supporters outside the presidential palace that she was leaving the residence, but that Kavelashvili had no legitimacy as president, which…