Pakistan's largest private bank is facing a $629 million penalty in the United States over accusations of non-compliance with financial standards and practices at its New York branch.

HBL, formerly known as Habib Bank Limited, came under the radar of New York's state Department of Financial Services (DFS) over the bank's financial practices in December 2015.

A press release from US financial authorities identified significant breakdowns in the branch's risk management and compliance with applicable federal laws, rules, and regulations relating to anti-money laundering compliance, including the Bank Secrecy Act.

In a letter to the Pakistan Stock Exchange on Monday, the bank accused the DFS of "still not appreciating or recognising the significant progress that HBL had made at its branch."

Its company secretary Nausheen Ahmad said the hefty fine -- which if imposed would be the largest ever penalty handed out to a Pakistan bank -- was "unjustified, capricious and unreasonable".

She vowed to "vigorously contest" the decision in US courts and announced it would be closing down its New York branch.

The State Bank of Pakistan issued a statement late Monday saying it was aware of the situation and that there were no immediate risks to HBL's operations and Pakistan's banking industry.

"State Bank of Pakistan reiterates its determination to protect the interests of depositors and to protect the health and safety of the country's banking system," it said.

HBL was founded in 1947 and now has over 40 percent of market share in Pakistan's banking sector.

It was part-privatised in 2004, with the Agha Khan Foundation buying the bulk of the shares.

In April 2015 the Pakistan government approved divesting all of its state-owned shares in HBL for $1.02 billion, in the country's largest-ever equity offering.

It had received a licence to open a branch in China last year, making it the first South Asian lender to operate in the world's number two economy.

It currently has more than 1,700 branches in Pakistan and an international network spread over 25 countries.