India's police have detained two employees of Punjab National Bank, the state-run lender that says it has been the victim of a $1.77 billion fraud.

These mark the first arrests in a fast-widening probe into the country's biggest-ever bank scam. 

Gokulnath Shetty and Manoj Kharat are suspected of steering fraudulent loans to companies linked to billionaire jeweller Nirav Modi and entities tied to jewellery retailer Gitanjali, which is led by Modi's uncle, Mehul Choksi. 

India's Income Tax department warned in an internal note seen by Reuters that domestic banks could take a hit of more than $3 billion from loans and corporate guarantees provided to Modi and Choksi. 

The arrests came after India's second-largest state-run lender said last week that it had been hit by massive fraud, sending its share price tumbling. 

The accusations against the two relatively junior PNB officials were detailed in the lender's disclosure, and also contained in a preliminary police report. 

The Central Bureau of Investigation (CBI) also arrested a third person, Hemant Bhat, whom a source described as the "authorised signatory" of the companies tied to Nirav Modi. 

A police source said six more PNB employees were "being examined" after the CBI conducted additional searches at the PNB's branch in southern Mumbai where the alleged fraud took place. 

Police sources say Modi, whose high-end jewellery has been worn by Hollywood stars including Kate Winslet, and Choksi left India last month and their whereabouts are unknown. 

Neither Modi nor Choksi have so far commented on the allegations.  

Gitanjali has previously denied Choksi's involvement in the fraud and said he would take "necessary legal action" to get his name removed from the police case. 

Meanwhile the Enforcement Directorate, India's financial crime agency, said over the weekend that it conducted additional searches at 21 locations of companies tied to Modi, seizing 250 million rupees ($3.89 million) in precious stones, metals and jewellery. 

Both authorities have conducted dozens of raids since PNB disclosed the fraud, targeting PNB, Modi and Choksi, with the Enforcement Directorate now having seized diamonds, gold and jewellery worth 56.7 billion rupees. 

A tax department spokeswoman told Reuters officials had seized 29 properties and 105 bank accounts linked to Modi.

The biggest bank fraud in India's history has sent rumbles through India's financial system, raising fears about the scale of problems in the banking sector that is already saddled with $147 billion of soured debt. 

PNB said it was running an audit of its systems to prevent a recurrence of such a fraud, but did not see a long-term hit to its operations. 

The bank, which has $120 billion in total assets, has lost more than a fifth of its market value since it disclosed the fraud. 

Scrutiny of banks' technical systems will intensify even further after India's City Union Bank over the weekend said it had suffered three "fraudulent remittances" of nearly $2 million that had been pushed through the SWIFT financial platform.

The case was reminiscent of the $81m cyber heist that hit Bangladesh's central bank in 2016.