Federal prosecutors in Brazil have opened a formal inquiry into possible "influence peddling" by former President Luiz Inacio Lula da Silva.

The investigation will look into whether Lula improperly used his connections overseas to benefit Latin America's largest engineering firm, Odebrecht.

In May, prosecutors in the capital Brasilia said they had opened a preliminary investigation into the matter, saying the former leader had frequently travelled abroad at Odebrecht's expense after leaving office, from 2011 until 2014.

The inquiry announced on Thurday puts the legacy of one of Brazil's most popular former leaders on the line at a time when some are calling for the impeachment of his chosen successor, President Dilma Rousseff, for alleged campaign finance irregularities.

A spokeswoman for Lula's institute, the Instituto Lula, said the institute was surprised by the news, and thought the inquiry had been escalated too quickly, the Reuters news agency said. She added that Lula's travels were completely legal.

In their preliminary inquiry, prosecutors cited media reports that Brazil-based Odebrecht had won contracts in countries including the Dominican Republic and Cuba after Lula met with their leaders, travelling at Odebrecht's expense.

Lula may have also improperly influenced Luciano Coutinho, president of the state-run development bank BNDES, when it approved loans for Odebrecht projects abroad, prosecutors said.

Speaker anger

Later on Friday, Eduardo Cunha, the speaker of Brazil's lower house of Congress, announced his break with Rousseff's government.

Cunha had earlier also been accussed of aiding Odebrecht. 

In a news conference in Brasilia, Cunha accused the Rousseff administration and prosecutor general Rodrigo Janot of conspiring to incriminate him in a broadening corruption scandal at state-run oil firm Petrobras.

The rift between Cunha and Rousseff does not necessarily mean an immediate departure of his PMDB party from the president's coalition, but Cunha said he would argue in favour of that.

The rupture, which has been in the works for months, comes a day after Cunha said was weighing legal arguments for impeachment.

As speaker of the house, Cunha would be responsible in Congress for initiating that process.

Al Jazeera's Kimberly Halkett, reporting from Brasilia, said that the scandal was widening by the hour. 

"Not only have we seen an investigation into a very popular former president, but Eduardo Cunho, another high profile politician with ties to the current president, has been accused of helping the same construction company for securing contracts," she said.

"It is a stunning revelation and very bad news for Dilma Rousseff as there have been calls for her impeachment.

"Although it is destabilising for her government, there is no proof that she has any connection with these allegations."

'Operation Car Wash'

Brazil's political and elite business circles have already been thrown into commotion by "Operation Car Wash," a huge investigation into a bribes-and-kickbacks network that saw companies, including Odebrecht, bribe politically connected executives at state oil giant Petrobras to grant inflated contracts.

Neither Lula or Rousseff, chairwoman of Petrobras for seven years, have been directly implicated in the scandal but there are mounting calls for Rousseff's resignation or impeachment.

Some of the money allegedly went into the ruling Workers' Party campaign coffers.

Plea bargain testimony from engineering executive Ricardo Pessoa, obtained by Veja magazine last month, said money originating from overpriced Petrobras contracts had helped finance Rousseff's 2014 re-election campaign.

Rousseff and her ruling Workers' Party say all campaign donations were legal and the president has urged a thorough investigation into corruption at Petroleo Brasileiro, as the oil major was formally known.

Source: Al Jazeera and agencies