However, since January, investigators have unearthed at least 47 million euros, or $61.4 million, that they say he stashed offshore, in Switzerland but also possibly in other countries.

The financial crimes unit of the Spanish police released a report in May in which it said that it had identified 19 of the fund’s corporate donors, which had received public contracts worth more than $15 billion from conservative politicians over a decade.

Last week, the newspaper El Mundo published ledgers it said were parallel financial accounts kept by the Popular Party. The information mirrored allegations made in late January by another Spanish paper, El País, which reported that the ledgers showed secret payments to Mr. Rajoy and other party members for nearly 20 years, ending in 2008, when Spain’s construction boom ended.

Mr. Rajoy and other party officials have denied wrongdoing, as has Mr. Bárcenas.

With a bulletproof majority in Parliament and elections not due until 2015, Mr. Rajoy is in little immediate danger of being nudged from power. But the persistent questions about the fund have pushed him and his inner circle toward blanket denials that leave them little room to maneuver if Mr. Bárcenas divulges more damning information or the investigation otherwise deepens.

Proving any illegal party funding is likely to be an uphill struggle, given the murkiness of rules governing the financing of Spanish parties — something that Mr. Rajoy’s government is in the process of tightening. But the questions have already helped sink Mr. Rajoy’s popularity to record lows. His government has also faced mass demonstrations, as citizens blame its austerity push for their worsening conditions and a record unemployment rate of 27 percent.

Only 23 percent of respondents would now vote for the Popular Party, according to a telephone survey by Metroscopia, a pollster, and published by El País this month. That is near the lowest level since Mr. Rajoy came to power in November 2011. Meanwhile, 86 percent of those surveyed said that they did not trust Mr. Rajoy. The survey was based on interviews with 1,000 adults and has a margin of sampling error of plus or minus 3 percentage points.

Still, the Socialists and other parties continue to trail the Popular Party, according to Metroscopia’s latest poll, showing the extent and depth of the discontent and mistrust in Spain, as politicians, the monarchy and almost every other institution have become entangled in the web of fraud investigations, many related to building contracts awarded before the bursting of the country’s construction bubble.