The complaint, registered with the Central Bureau of Investigation (CBI) earlier in the week according to a copy seen by Reuters on Thursday, widens the scope of the investigation into what has been dubbed the biggest bank fraud in Indian history.
Last month, Punjab National Bank (PNB) and authorities accused two jewellery groups - one controlled by Mr Modi and the other by his uncle, Mehul Choksi - of colluding with rogue bank employees to secure credit from overseas lenders using fraudulent guarantees for the past eight years.
Both Mr Modi and Mr Choksi have denied wrongdoing, and so have two key accused PNB employees in the case, which has so far led to 19 people being arrested. The whereabouts of Mr Choksi and Mr Modi, who police say left India before the first complaint was filed, are unknown.
The latest CBI complaint names Mr Modi's flagship Firestar company - which previously said it had no involvement in the allegations levelled against him - for the first time. Three of his other firms were named in the original complaint.
PNB said that it had been cheated of a further 3.22 billion rupees ($49.4 million) in the new complaint filed on March 4. It alleges that the credit sanctioned to Modi's Firestar group of companies was not used for the purposes for which it was given.
There was no immediate comment from Firestar.
PNB also alleged it has uncovered fraudulent transactions between the Firestar group of companies and other entities controlled by Mr Modi.
Vijay Aggarwal, a lawyer for Mr Modi, dismissed the new complaint as "contrary to law", saying any such allegations should have been part of the initial police case.
The new disclosure pushes PNB's total exposure to more than $2 billion. The bank initially reported to authorities on Jan. 29 that the jewellery groups had defrauded it of about $44 million. On Feb. 14 it said the fraud sum had reached $1.77 billion after a detailed investigation. It raised the amount further to nearly $2 billion last week.
A source and documents reviewed by Reuters on Tuesday showed the amount involved in the fraud was likely to rise above the $2 billion mark.
Separately Mr Choksi, in a March 7 dated letter, has accused the Central Bureau of Investigation (CBI), one of the lead agencies probing the fraud, of gross abuse of due process.
In his letter to the CBI, a copy of which was reviewed by Reuters on Thursday, Mr Choksi said the seizure of his assets, bank accounts and the shutting down of all his offices in India had caused prejudice against him.
Mr Choksi, whose passport has been suspended, said he feared greatly that he would not get "fair treatment and a fair trial" if he returned.
"The investigating agencies are acting with a pre-determined mind which is hampering the process of law and interfering with the course of justice," he wrote in the letter.
A CBI spokesman said the agency was not concerned about Mr Choksi's allegations and that authorities were ready to facilitate the required documents for him to travel back to India. "The investigation is going on and he should join the investigation," the spokesman said.
Mr Choksi, whose Gitanjali Gems operates stores under banners including Gili, Nakshatra and Asmi, said in his letter that while the CBI has seized his assets, it has yet to submit a "Seizure Memo" in court, as required by law.
Local media reported last week that a Mumbai court issued non-bailable arrest warrants against Mr Modi and Mr Choksi following an appeal by the Enforcement Directorate, an Indian agency focused on foreign exchange and money laundering offences.
Mr Choksi said in the letter he had travelled abroad on business before the complaints were made and his departure was not "a direct result" of the allegations against him.
He added in the letter that he had undergone a cardiac procedure during the first week of February and he was unable to travel for at least four to six months as the procedure was yet to be completed. He did not say where he was.