(Repeats May 16 story with no changes to text)

* India rates steady on modest demand

* Vietnam prices rise to $585-$590 per ton

* Thai prices hit over a 3-month peak

May 16 (Reuters) - Thailand's rice export prices rose to a more than three-month peak this week, bolstered by thin supplies and strong demand, while top exporter India's rates remained steady due to lacklustre demand.

Thailand's 5% broken rice prices continued to climb, reaching $632 to $640 per metric ton from last week's price of $600.

The price increase is due to diminishing supplies, said a Bangkok-based trader, adding that there was strong demand from Indonesia and flood-hit Brazil.

The flooding of farmland and towns in southern Brazil has killed people, livestock, crippled infrastructure and is hampering shipping of grains to local processors and the Rio Grande port.

Domestic demand and activity were also bustling and new supply would come in July, said another Bangkok-based trader.

India's 5% broken parboiled variety was quoted at $531-$539 per metric ton this week, unchanged from the last week.

"Indian prices are (more) competitive than other destinations but still demand is not picking up," said an exporter based in the southern state of Andhra Pradesh.

Meanwhile, Vietnam's 5% broken rice was offered at $585-$590 per metric ton on Thursday, up from $585 a week ago, traders said.

"Demand remains strong while domestic supplies are running low," a trader based in Ho Chi Minh City said, adding that Indonesia's state food procurement agency Bulog is seeking to buy more rice.

Traders said supplies will improve from June when the summer-autumn harvest begins. (Reporting by Daksh Grover in Bengaluru, Rajendra Jadhav in Mumbai, Chayut Setboonsarng in Bangkok, Khanh Vu in Hanoi; Editing by Eileen Soreng )