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.
Mr 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 Mr Barcenas ran a PP slush fund that took donations from construction magnates and distributed them to party leaders in cash.
Mr 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, Mr Barcenas for the first time admitted that the handwriting in the ledger was his.
He 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 Mr 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 Mr Rajoy of 2.1m pesetas (12,600 euros; Â£11,000) 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 pulverise the alibi used until now by the PP to deny the authenticity of its ex-treasurer's papers," El Mundo said.
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 recognise them as the accounts of this political organisation."
This is another twist in possibly the most important corruption scandal to hit modern Spanish politics, says the BBC's Tom Burridge in Madrid.
The allegations have caused anger among Spaniards already suffering a deep and long recession and biting austerity cuts.
A Spanish newspaper has published what it alleges are documents showing Prime Minister Mariano Rajoy and other top politicians received illicit payments.