The affair threatens to destabilize Rajoy's government as it works to strengthen the public finances of the eurozone's fourth-biggest economy, anxiously watched by its neighbours since he took power in 2011.
Rajoy, 58, has denied receiving illegal payments from his Popular Party and refused to step down. The allegations come from the party's former treasurer, Luis Barcenas, who has named him in the scandal.
After months of incriminating leaks in the press and under pressure from political opponents who threatened a no-confidence vote, Rajoy bowed to calls to explain himself publicly.
"I want to give an explanation and recount everything that has happened and give my side of the story... to all the citizens," he said on July 22.
His appearance would focus not only on the Barcenas affair but on Spain's economic outlook, which has improved recently, he added.
That provoked warnings from opponents that he might try to bury the Barcenas issue under the economic news in his parliamentary appearance.
Second-quarter data showed Spain's huge unemployment rate eased to 26.3 percent from over 27 percent, while the monthly economic contraction slowed to 0.1 percent of output from 0.5 percent.
The corruption affair originated in 2009 as a judicial investigation into alleged kickbacks involving members of the Popular Party.
It exploded in January when a newspaper published copies of account ledgers purportedly showing irregular payments to top party members, including Rajoy who has led the party since 2004.
Those allegations sparked outrage among ordinary Spaniards struggling with spending cuts that Rajoy has imposed during a deep recession.
Barcenas was jailed in July pending an investigation into a separate corruption case, in which he is alleged to have held secret Swiss bank accounts.
On July 14 centre-right daily newspaper El Mundo published friendly text messages purportedly sent by Rajoy to Barcenas from May 2011 to March 2013, some two months after the scandal erupted.
That reignited calls by the opposition Socialists for him to step down, but a defiant Rajoy told reporters: "I will fulfill the mandate the Spanish people gave me."
He vowed to "defend political stability" as he steers Spain out of its deep recession.
The noose appeared to tighten around him when Barcenas testified in court that he handed cash to Rajoy and the party's deputy leader Maria Dolores de Cospedal.
Conservative newspaper El Mundo calculated that Barcenas paid a total of €343,700 euros to Rajoy over two decades.
Cospedal has been summoned to testify as a witness on August 14 by the judge investigating the scandal, Pablo Ruz. She has rejected Barcenas's claims as lies.
In a poll published on July 21 in El Mundo newspaper, nearly nine out of 10 Spaniards questioned said they felt Rajoy should explain himself in parliament.
Two-thirds believed Rajoy had received payments, with one in five believing the contrary.
Political analysts say it is unlikely Rajoy will step down however. Such resignations have been very rare in Spanish politics since the restoration of democracy in 1978.
Spain's opposition socialist PSOE party on Wednesday reiterated their call for Rajoy to step down.
"Our aim is two-fold: that the prime minister tell the truth and that he quit his post," its deputy leader Elena Valenciano told reporters.
"If we don't get that tomorrow, we will keep insisting and fighting for it."
Government sources told Spain's conservative ABC newspaper that Rajoy would be "calm" during a grilling Spanish daily El Pais expected to be "intense".
Those sources told ABC the Spanish leader would focus on the "irresponsibility" of the opposition for "having put Spain's political stability at risk" by focusing on the corruption scandal.
The paper also said Rajoy wouldn't go into depth about the corruption scandal involving Barcenas as the case was still in the courts.
Thursday's session in parliament was due to start at 9am (0700 GMT).