MUMBAI, May 16 (Reuters) - The Indian government announced a third buy back of bonds this month after the first two attempts were met with a tepid response.

The central bank said it would buy back 600 billion Indian rupees worth of securities, maturing this financial year, on May 21.

The securities offered for buy back are 7.35% 2024, 8.40% 2024, floating rate bonds (FRB) 2024 and 9.15% 2024, the Reserve Bank of India said in a statement.

Earlier in the day, the central bank accepted bids to buy back only 20.7 billion rupees ($247.96 million), a fraction of the total buyback of 600 billion rupees offered.

"Most banks are out of money on these bonds. Why will anyone want to sell these bonds at a loss," a senior treasury official at a large state-run bank said.

"They can easily hold these bonds till maturity and get the face value at least," the person added.

In a previous auction on May 9, the central bank accepted bids to buy back government bonds worth 105.1 bln rupees, far below the notified amount of 400 billion rupees.

The choice of new securities offered for buy back is better than the last two, as they are in the money, so at least chances of success rise, a trader with a private bank said.

The central bank can choose to accept the higher prices demanded by the banks if it was looking at purely infusing cash into the banking system, but that would also push down yields for these papers by a large margin.

"They would not want to accept higher prices being demanded and do a 25 basis points rate cut without actually cutting rates," the senior treasury official added.

($1 = 83.4823 Indian rupees) (Reporting by Bhakti Tambe, Dharamraj Dhutia and Siddhi Nayak; Editing by Eileen Soreng and Shinjini Ganguli)