El Mundo said it had original ledger entries handwritten by the former treasurer of the governing Popular Party (PP), Luis Barcenas.
It said it had delivered the documents to the High Court.
Mariano Rajoy and other PP members have repeatedly denied that they received illegal payments.
Another Spanish paper, El Pais, published similar documents earlier this year.
It is claimed that Luis Barcenas ran a PP slush fund that took donations from construction magnates and distributed them to party leaders in cash.
Luis Barcenas is in custody facing trial for corruption and tax fraud. He denies the allegations.
However, in an interview published in El Mundo on Sunday, Luis Barcenas for the first time admitted that the handwriting in the ledger was his.
Luis Barcenas added that the photocopies originally published by El Pais were a fraction of the documents he had in his possession.
El Mundo said the documents it had seen showed that Mariano Rajoy received payments in 1997, 1998 and 1999 when he was a minister in the government of Jose Maria Aznar.
They included, it said, two payments to Mariano Rajoy of 2.1 million pesetas (12,600 euros; $16,000) in 1998.
The alleged payments are said to have been undeclared and untaxed.
Spanish opposition leader Alfredo Perez Rubalcaba in February called on Mariano Rajoy to resign over the allegations.
“The Luis Barcenas originals published by El Mundo today pulverize the alibi used until now by the PP to deny the authenticity of its ex-treasurer’s papers,” the newspaper wrote.
The PP responded with a statement saying: “The Popular Party reiterates that it does not know of the notes nor their content, and it does not in any way recognize them as the accounts of this political organization.”
The allegations have caused anger among Spaniards already suffering a deep and long recession and biting austerity cuts.
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