Economy Minister Luis de Guindos said he did not think the scandal was affecting investor confidence in Spain.
The revelations come as Spain, after a year of soaring borrowing costs, begins to show signs of convincing investors and European authorities that it is serious about reforming the economy and keeping its finances in check so it does not need a bailout.
Last week Rajoy said he would deal firmly with anyone found to have accepted money under the table.
The scandal broke when the National Court reported recently that Barcenas amassed an unexplained â¿¬22 million ($30 million) in a Swiss bank account several years ago.
Barcenas, who served in the party's treasury for 20 years, resigned in 2009 after he was named in a National Court probe into alleged irregular financing practices by the party.
His lawyer denies the Swiss account money was illegally obtained or linked to party.
The lists published by El Pais include the names of former ministers Angel Acebes, Javier Arenas and Francisco Alvarez Cascos. The paper said the documents showed that as of 1997 Rajoy received some â¿¬25,000 each year.
The paper said each of the party members listed and the businesses named denied receiving or making the payments shown.
Many of the payments occurred during Spain's boom years of the late 1990s when the Popular Party was in power and the construction industry made the country one of the most successful economies in the European Union.
The corruption scandal is the latest to rock Spain, with dozens of other cases involving bankers, politicians, town councilors and even the royal family. But this one has shocked people more given that Rajoy and his party are demanding enormous sacrifices of Spaniards as the country battles recession and 25 percent unemployment.