The firm has so far bought back 26.82 lakh equity shares since the start of the offer, it said in a statement.
Reliance Infrastructure bought back two lakh equity shares today.
Earlier, shareholders of the company had approved the buyback of equity shares up to an aggregate amount of Rs 2,000 crore.
The last date for the buyback is March 4, 2009, a year from the date of the board's approval for the offer.
Shares of the company closed at Rs 1,442.30 at the BSE, down 4.92 per cent from the previous close.