"The Popular Party has nothing to fear, our books are clean," said Carlos Floriano, the party's deputy national organizer.
The newspaper El Mundo on Sunday published what it said were friendly text messages from recent months between Rajoy and Luis Barcenas, a top member of the party's treasury department for some 20 years until he resigned in 2009.
Barcenas is at the heart of a probe into a slush-fund that allegedly made payments to top Popular Party figures, including Rajoy.
Rajoy, who has denied that he or other party figures received illegal payments, faced a likely barrage of questions at a press conference later Monday with visiting Polish counterpart Donald Tusk.
Barcenas was jailed last month while he awaits possible trial on tax fraud and money-laundering charges after the National Court found he had accumulated some 47 million euros ($61 million) in secret Swiss bank accounts.
On Monday, he appeared before a judge investigating his suspected role in the slush fund probe. The leading daily El Pais said he admitted the authenticity of ledger sheets published by El Mundo last week that allegedly document under-the-table payments to party leaders, among them Rajoy.
El Mundo said last week the documents showed Rajoy received at least 42,000 euros in payments while serving as a minister between 1997 and 1999.
The mobile phone text messages published by the paper Sunday date from before Barcenas was sent to jail. In them Rajoy allegedly tells the former treasurer to stay calm but advises him that the situation is difficult.
Floriano denied Monday that the party was trying to negotiate a deal with Barcenas.
"The party has not accepted, and will not accept, any blackmail," said Floriano.
"It's Barcenas who is in jail and it's up to him to explain where he got the money in Switzerland from," he said.
Barcenas initially claimed the money stemmed from private business deals. But last week El Mundo cited him as saying the Popular Party has long been illegally funded.
The allegations have rocked the country, coming as people cope with harsh austerity measures and tough economic reforms aimed at reducing debt while unemployment is 27 percent.
Spain has been in recession for most of the past four years.
Economy Minister Luis de Guindos, however, dismissed suggestions that the scandal was affecting the county's image economically.
"As regards international investors, nobody has asked me about this," he said pointing out that Spain's bond prices and stock exchange index had not fluctuated greatly Monday.