He batted off calls from his political opponents to step down over allegations that he received secret payments through his Popular Party when he was a government minister in the late 1990s.
Pressure intensified on Rajoy, 58, when the man accused of organizing the payments, the party's jailed former treasurer Luis Bárcenas, went before a judge investigating the scandal following fresh allegations in the press.
"I will fulfil the mandate the Spanish people gave me," a defiant Rajoy told reporters, however, vowing to "defend political stability" as he steers Spain out of a deep recession and fights to stabilize its public finances.
The Prime Minister has denied any wrongdoing in the growing controversy, which first erupted in January when a newspaper published copies of account ledgers purportedly showing irregular payments to top party members. Further leaks of supposed party accounts later implicated Rajoy himself.
Rajoy pointed to the commanding parliamentary majority he has enjoyed since leading the party to a landslide electoral victory in November 2011, which has enabled him to push through tough economic reforms.
Media have been speculating for weeks that Bárcenas, who is in jail in a separate corruption probe, might try to pressure Rajoy with the threat of fresh leaks, but the Prime Minister said he had no fear of "blackmail" and that he trusted the courts to do their job.
"The state of law will not submit to blackmail," he said on Monday, at a news conference alongside visiting Polish Prime Minister Donald Tusk.
The noose had appeared to tighten on Rajoy on Sunday when the conservative newspaper El Mundo published friendly text messages he purportedly sent to Bárcenas from May 2011 to March 2013, some two months after the scandal erupted.