Bad loans held by Indian banks are still rising sharply, India's central bank said Tuesday, as it warned the country's lenders face "significant challenges".

The Reserve Bank of India (RBI) noted in its Financial Stability Report that gross non-performing assets at Indian banks stood at 7.6 percent of their total in March 2016, up from 5.1 percent in September.

Outgoing RBI governor Raghuram Rajan has made cleaning up the banking sector's mountain of soured loans -- defined as in default or close to it -- a priority of his tenure.

The report comes after India's finance minister Arun Jaitley pledged earlier this month to protect state banks suffering from mounting bad loans to bolster the country's financial system.

"India's financial system remains stable, even though the banking sector is facing significant challenges," the RBI said in its report.

The RBI last year ordered banks to undertake an Asset Quality Review -- forcing lenders to classify many more loans as soured -- and set a 2017 deadline for them to clean up their balance sheets.

Jaitley has said the government would earmark 250 billion rupees ($3.7 billion) for the recapitalisation of banks this year and would provide more if needed.

Vijay Mallya, a liquor tycoon who left the country in March owing $1.34 billion, has come to personify India's problems with bad debt, with banks scrambling to recover loans to his now-defunct Kingfisher Airlines.

Rajan is stepping down from the RBI in September after three years at the helm. His successor has yet to be announced.