RIO DE JANEIRO — Brazil’s Public Ministry, a body of independent public prosecutors, has begun an investigation into a claim connecting former President Luiz Inácio Lula da Silva to a vast vote-buying scheme that involved the channeling of funds to the governing Workers’ Party. The inquiry, which was announced in the capital, Brasília, on Friday and comes after several months of analyzing testimony, opens a new phase in what has arguably been Brazil’s largest corruption scandal, already involving the conviction of Mr. da Silva’s powerful former chief of staff, José Dirceu de Oliveira e Silva, on conspiracy and bribery charges last year. The move by the Public Ministry, which asked the federal police to carry out the investigation, is thought to be the first time that Mr. da Silva has been directly investigated in connection to the scheme, called the mensalão, or big monthly allowance, for the regular payments that some lawmakers received. The scandal emerged in 2005, during Mr. da Silva’s first term as president. At 67, he remains a towering figure in Brazilian politics.