RIO DE JANEIRO — Brazil’s political establishment was shaken on Friday by the news that federal prosecutors had opened an influence-peddling inquiry into the business activities of Luiz Inácio Lula da Silva, the former president who presided over Brazil’s emergence this century as a leading power in the developing world.

The report comes at a difficult time for the governing Workers Party, with Mr. da Silva’s protégé and successor, Dilma Rousseff, struggling with calls for her impeachment over a bribery scandal at the national oil company. Mr. da Silva, 69, was among the founders of the party in 1980.

The inquiry by a special anticorruption unit of the Public Ministry, a body of independent prosecutors, is reportedly delving into Mr. da Silva’s ties to Odebrecht, one of Brazil’s largest construction companies. That the inquiry, a preliminary step before deciding whether to open a broader investigation, had opened in recent days was first reported by the Brazilian magazine Época.

The prosecutors are examining whether Mr. da Silva improperly used his influence as a former president and one of Brazil’s most powerful political figures to obtain loans from Brazil’s national development bank, a state-controlled financial institution with a lending portfolio larger than that of the World Bank, for Odebrecht’s dealings in Cuba and the Dominican Republic.