A lawmaker from the northern Spanish city of Palencia, Pablo Casado has been a member of the People's Party since 2003.
The parliamentary vote seeking Rajoy's ouster was filed by the main opposition Socialists, who say he has lost credibility.
Spanish Prime Minister Mariano Rajoy vowed on Wednesday not to resign ahead of a no-confidence vote in parliament on Friday over graft convictions against members of his conservative Popular Party.
Spain last year surpassed the United States to become the world's second most visited country after France, Spanish Prime Minister Mariano Rajoy said during a visit to Italy.
Spanish Prime Minister Mariano Rajoy said in a newspaper interview that Spain would not be divided, a week after Catalonia held a referendum that authorities there say showed voters overwhelmingly support independence.