By Paul Kiernan, Paulo Trevisani and Luciana Magalhaes 

RIO DE JANEIRO--A corruption dragnet that has jailed dozens of executives and erased billions from Brazil's state-controlled oil giant has now snared some of the nation's top lawmakers, deepening a crisis that is weighing on South America's largest economy.

Brazil's Supreme Court on Friday gave the go-ahead to federal prosecutors to investigate 47 politicians, including Senate President Renan Calheiros and Eduardo Cunha, head of the Chamber of Deputies, as part of a widening corruption probe of Petróleo Brasileiro S.A., known as Petrobras.

Both men are members of the PMDB party, Brazil's largest and a key partner in President Dilma Rousseff's effort to pass austerity measures to narrow a yawning budget gap. With the economy skidding and Brazil in danger of losing its investment-grade sovereign rating, the investigation could push top legislators away from further tax increases and program cuts that have proved unpopular with the public.

"As for me I will give all explanations in the light of day and provide whatever information the courts desire," a post on Mr. Calheiros's official Twitter account said. A post on Mr. Cunha's Twitter account said the investigation "deserves due response as soon as I have knowledge of its content."

Fear that fallout from the scandal would threaten budget cuts has weighed on Brazil's stocks and currency. The Ibovespa stock index declined by 3.1% this week, while the real plunged about 7%, closing at 3.0536 reais to the dollar on Friday.

On Tuesday, hours after rumors emerged that his name was on the list, Mr. Calheiros rejected an executive order from Ms. Rousseff that would have increased payroll taxes to fill government coffers.

Local press characterized the move as retaliatory, though it followed a period of heightened tension between the two politicians. The attorney general is independent of the government.

"What happened this week is that the risks, which were already there, became more visible," says Carlos Melo, a professor at São Paulo business school Insper. "After Renan's move, it is clear the government won't be able to push any kind of fiscal adjustment through Congress without negotiating first." In practice, analysts say, that stretches the odds of the government meeting its 1.2% target for the primary budget surplus, seen by many as a make-or-break goal in the effort to avoid a sovereign downgrade.

Prosecutors say the PMDB, Ms. Rousseff's Workers' Party, and other government-aligned parties suggested executives to run major divisions at Petrobras.

One of the suspects, Paulo Roberto Costa, testified last year as part of a plea bargain that he had been chosen by Brazil's Progressive Party to head Petrobras' downstream division in 2004. During eight years on the job, Mr. Costa said, he approved multibillion-dollar contracts for refineries and other projects that he knew had been inflated by a "cartel" of construction companies. The companies then kicked back 3% of the value of the contracts, on average, to Mr. Costa and party officials, he said.

Petrobras has said it considers itself a victim in the scheme. The construction firms alleged to have been involved either have declined to comment, denied wrongdoing or have said they were cooperating with investigators.

In all, Mr. Zavascki cleared prosecutors to investigate members of five parties. Other politicians named to the list are former Mines and Energy Minister Edison Lobão, Senator Gleisi Hoffmann, who was also Ms. Rousseff's former chief of staff, and former President Fernando Collor de Mello. Also included on the list was Workers' Party Treasurer João Vaccari Neto, whom Federal Police questioned last month in connection to the investigation. None could be immediately reached for comment.

The Worker's Party said in a statement Friday night that the party only receives lawful donations. It said accusations made in plea bargains aren't to be trusted, and the party will prosecute the authors of "lies."

The scandal has crippled Petrobras: The company's chief executive resigned last month, its stock has fallen around 62% since September and Moody's downgraded its debt to junk status last month. Because of difficulties calculating corruption-related losses, auditors haven't signed off on Petrobras' financial statements since mid-2014.

That has effectively cut the firm off from global credit markets, forcing it to slash investments and sell assets. The oil giant has canceled projects and delayed some payments to accused construction companies. That in turn has set off a wave of credit downgrades and layoffs that is rippling across the economy.

Write to Paul Kiernan at paul.kiernan@wsj.com, Paulo Trevisani at paulo.trevisani@wsj.com and Luciana Magalhaes at Luciana.Magalhaes@dowjones.com

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