(Reuters) — Brazilian construction firm Odebrecht S.A. and affiliated petrochemical company Braskem S.A. pleaded guilty in a U.S. court on Wednesday to violating American foreign bribery laws as part of a $3.5 billion deal resolving a sweeping corruption probe of Brazil's state oil company.

The companies entered their pleas in federal court in Brooklyn in the major corruption case stemming from a wide-ranging probe into their role in a scheme involving political kickbacks at Brazil's Petrobras.

The cumulative penalties, some of the largest ever paid in a foreign corruption case, were negotiated as part of a global settlement with U.S., Brazilian and Swiss authorities.

Odebrecht is Latin America's biggest engineering firm. Braskem is jointly owned by Odebrecht and Petrobras.

Their guilty pleas were the first in the United States following an investigation in Brazil dubbed "Operation Car Wash" into corruption at Petrobras, which has led to dozens of arrests and political upheaval in Brazil.

In court on Wednesday, Odebrecht agreed that it has the ability to pay $2.6 billion. Sentencing in the case was scheduled for April, when the deal would become finalized.

Under the global settlement deal, Braskem also has agreed to pay $957 million, according to the U.S. Securities and Exchange Commission. Braskem agreed to pay more than $632 million in criminal penalties and fines as well as additional money to the SEC and Brazilian authorities, the SEC said.

Odebrecht agreed that the appropriate criminal fine is $4.5 billion, but that will be subject to further analysis of the company's ability to pay that amount, the U.S. Justice Department said.

Both companies also agreed to cooperate with authorities, implement compliance improvements and become subject to oversight by external monitors.

The total fines and penalties paid out by the companies exceeded a 2008 agreement in which German engineering company Siemens paid $1.6 billion to U.S. and European authorities for paying bribes to win government contracts.

Prosecutors in Brazil have said more than $2 billion in bribes were paid over a decade, mainly to Petrobras executives, from construction and engineering companies.

Among those charged have been former Brazilian President Luiz Inacio Lula da Silva, who Brazilian prosecutors say oversaw a scheme in which Odebrecht paid 75 million reais ($22.18 million) in bribes to win eight Petrobras contracts.

Odebrecht's former CEO, Marcelo Odebrecht, is already serving a 19-year sentence after being found guilty on corruption charges in Brazil last year. He turned state's witness and is expected to be freed by the end of 2017.

The nearly three-year "Car Wash" investigation, named for a Brasilia gas station where some of the alleged money laundering took place, also contributed to the downfall of Brazil's former president, Dilma Rousseff. She was ousted by Brazil's Senate in August, ending an impeachment process that polarized Latin America's biggest country amid the massive corruption scandal and a brutal economic crisis.

Michel Temer, Rousseff's vice president, then took over, but several members of his cabinet and the leader of his Brazilian Democratic Movement Party have been either charged with graft or accused of it.

Mr. Temer himself has been cited in recently leaked testimony that Odebrecht officials have given, reportedly accused of accepting illegal campaign donations, allegations he has denied.