(This story corrects name of prosecutor in fourth paragraph to Lima from Limas)
By Caroline Stauffer and Walter Brandimarte
SAO PAULO (Reuters) - Brazilian police on Friday arrested Marcelo Odebrecht, the head of Latin America's largest engineering and construction company Odebrecht SA, and accused his family-run conglomerate of spearheading a $2.1 billion bribery scheme at state-run oil firm Petrobras.
Police also apprehended Otavio Marques Azevedo, CEO of Andrade Gutierrez, Brazil's second-largest builder, as the probe into corruption at Petrobras spread to the highest level of Brazilian business.
Odebrecht, Azevedo and other top executives arrested in Sao Paulo were driven to the airport in a van and flown to the southern city of Curitiba, where Brazil's largest-ever corruption scandal is being investigated.
A lead prosecutor, Carlos Fernando dos Santos Lima, said he had "no doubt" Odebrecht and Andrade Gutierrez led what he called a "cartel" that overcharged Petrobras for work and passed on the excess funds to executives and politicians.
The arrest of 46-year-old Odebrecht, who has personal ties to former President Luiz Inacio Lula de Silva, could bring the scandal closer to the political heart of the ruling Worker's Party.
"There is a larger connection between Lula and Odebrecht and we see (Odebrecht's) possible indictment as a big risk," said Cameron Combs, Latin America researcher with Eurasia Group.
President Dilma Rousseff, who ran the board of Petrobras during Lula's presidency, has denied knowledge of corruption and urged a thorough investigation. Neither she nor Lula have been implicated.
Last month federal prosecutors opened a separate investigation into whether Lula improperly used his connections to benefit Odebrecht, saying he had frequently traveled abroad at Odebrecht's expense since 2011.
Lula's institute, the Instituto Lula, denied wrongdoing at the time and declined to comment on Friday.
Odebrecht was the third-generation leader of the privately held company and has been instrumental in the company's expansion throughout Latin America, Africa and the United States. Newton de Souza, previously Odebrecht's head of Fiduciary Affairs and Governance, will serve as interim CEO, according to an internal memo seen by Reuters.
Paulo Oliveira Lacerda de Melo will coordinate engineering operations, the memo said.
A lawyer for Marcelo Odebrecht did not return calls seeking comment. It is not known if Odebrecht or Azevedo will seek plea deals with prosecutors, as 17 other suspects have done.
Odebrecht SA said in a statement that the arrests were "unnecessary" because it was collaborating with investigators.
Odebrecht bond prices fell on Friday. Shares of Braskem SA, a petrochemical producer Odebrecht controls, were the worst performer on Brazil's Bovespa index as they slumped 10 percent.
Andrade Gutierrez said it was also cooperating with the investigation, but had no connection to the alleged corruption at Petrobras.
Neither Azevedo nor Odebrecht have been charged, and it was not clear how long they would be detained. Arrests of other top Brazilian executives resulted in months-long pre-trial incarceration in Curitiba.
The so-called Lava Jato probe, centered on Petroleo Brasileiro SA, as the oil major is formally known, has led to the indictments of more than 100 people and implicated dozens of lawmakers, most of them from Rousseff's Workers' Party.
The treasurer of the Workers' Party is currently in jail awaiting trial for corruption, although the party denies campaign donations it received were bribes.
Eight engineering companies under investigation donated 64.6 million reais ($20 million) to Rousseff's re-election campaign in 2014, almost double donations to her challenger, according to the electoral court. Andrade Gutierrez donated 21 million reais to Rousseff's campaign.
Federal judge Sergio Moro said investigators had evidence Odebrecht paid bribes "in a more sophisticated way" than other contractors, using overseas accounts.
The scandal has blocked the construction firms, including Odebrecht and Andrade Gutierrez, from doing business with Petrobras and economists say the subsequent paralysis is contributing to Brazil's descent into recession.
Brazil's Vice President Michel Temer said there "must have been a reason" to arrest the executives but that it was important to distinguish between the executives and the companies, which are major employers in Brazil.
The arrests, although somewhat expected, raised hopes among Brazilians that the investigation would not spare the elite in a country where the wealthy have enjoyed relative impunity.
"The objective of the operation is to bring a clear message that the law applies to everyone, no matter the size of the company, its place in society or its economic power," federal police agent Igor Romario de Paula said.
($1 = 3.1 Brazilian reais)
Additional reporting by Sergio Spagnuolo in Curitiba; Aluisio Alves, Asher Levine and Eduardo Simoes in Sao Paulo; Jeb Blount in Rio de Janeiro and Alonso Soto and Anthony Boadle in Brasilia; Editing by Mary Milliken, W Simon and Andrew Hay