March 11, 2014 1:11 p.m.

SÃO PAULO—Brazil’s federal tax authority filed a series of new tax claims against state-run energy company Petróleo Brasileiro SA, or Petrobras, between October and January, underscoring a recent surge in possible liabilities from the company’s legal and tax disputes.

Petrobras is challenging five tax assessments that total 8.77 billion Brazilian reais ($3.74 billion), according to a prospectus the company filed with the U.S. Securities and Exchange Commission on Monday.

It wasn’t clear whether the new claims were included in the BRL71.2 billion of “contingent” tax liabilities reported by Petrobras at the end of 2013, a figure that itself was up 41% from a year earlier. The firm couldn’t immediately comment.

In the prospectus, Petrobras said it has presented its defense against each of the claims and is awaiting judgment. The company considers the chance of losses to be “possible, but not probable, and accordingly we have not established any provision.”

But that doesn’t mean investors should brush the claims off. In November, Brazilian mining titan Vale SA VALE5.BR +0.77% settled a similar series of disputes over taxes on its foreign operations after authorities offered the company a discount on interest and penalties.

Vale agreed to pay BRL22.33 billion, contributing to a record $6.45 billion net loss in the fourth quarter. It managed to minimize the deal’s future impact by paying a portion of the taxes up front and extending the rest over 15 years.

Petrobras’s shares fell 2.3% Monday despite the bond sale and recently traded down 0.3% at BRL12.97, on track for its lowest close since 2005.

The latest tax assessments against Petrobras date to 2009. They include financial-transactions taxes for intercompany loans among Petrobras subsidiaries, taxes on the affreightment of oil platforms, taxes on profits by certain subsidiaries headquartered abroad, and social-security contributions on some employee benefits.

Luana Helsinger, an analyst at GBM in Rio de Janeiro, said Petrobras will likely end up paying some, but not all, of the back taxes.

“The tax agency isn’t going to forget about 8.8 billion reais, but I can’t quite imagine the entire amount being paid,” Ms. Helsinger said. She noted that Petrobras is already being forced by the government to subsidize gasoline prices and develop hugely expensive oil fields off Brazil’s coast. “Petrobras has a lot of bargaining power.”