The auction will be conducted on NSE's e-bid platform from 1530 hrs to 1730 hrs, after the close of market hours.
The debt auction quota gives overseas investors the right to invest in debt, up to the limit purchased.
According to the latest data with depositories, total investment in government debt has reached Rs 1,33,051 crore till yesterday, which is 95.04 per cent of total permitted limit of Rs 1,40,000 crore.
Consequently, the exchange has decided to conduct an auction for the allocation of unutilised debt limits on June 27.
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Last two auctions conducted by the exchanges for government debt securities witnessed lukewarm response after months of oversubscription.
The government debt securities attracted bids worth Rs 4,011 crore from foreign investors as against Rs 4,046 crore put on offer in an online auction on June 6.
Prior to that, it had attracted bids worth Rs 2,957 crore as against securities worth Rs 3,340 crore put on offer in the auction conducted on May 16.
To boost foreign funds inflows, the limit for overseas investors in central government bonds was hiked to Rs 1.4 lakh crore from April 4 and it will be further increase to Rs 1.44 lakh crore from July 5. Earlier, the limit was Rs 1,35,400 crore.