* Vietnam's rates unchanged at $580 per ton

* Bangladesh rice prices stay elevated

April 12 (Reuters) - Prices of rice exported from Thailand rose this week, supported by strong demand from Indonesia, while subdued demand kept Indian rates near a two-month low.

Thailand's 5% broken rice prices was quoted at $585 to $590 per ton, up from last week's $570.

Prices strengthened from last week due to demand from Indonesia, said a trader.

New supply was still being harvested, said another trader, adding that prices were supported by demand from Indonesia, where buyers were sourcing from Thailand, Vietnam and Pakistan.

Top exporter India's 5% broken parboiled variety was quoted at $540-$548 per ton this week.

Prices hit a record high of $560 last month after customs officials changed the calculation method for the 20% export duty, resulting in a higher levy.

"In the local market, supplies are sufficient, but demand has slowed from Asian and African buyers in the past few days," said a Mumbai-based exporter.

Indian exporters have received notices from the customs department demanding payment of duty differentials on rice exported in the last 18 months, four exporters told Reuters, a rare tax demand that could cripple rice shipments from India.

Vietnam's 5% broken rice were offered at $580 per metric ton on Thursday, unchanged from a week ago, traders said.

"Domestic paddy prices, however, are edging up slightly as supplies have shown signs of shrinking, while the intrusion of salt water in some Mekong Delta provinces is threatening rice production there," said a trader based in Ho Chi Minh City.

Vietnam's rice exports in the first quarter rose 17.8% from a year earlier to 2.18 million tons, according to the government's customs data.

Meanwhile, rice prices in Bangladesh stayed elevated despite good yields and record reserves, promoting the government to allow private traders to import nearly 100,000 tonnes of rice to control prices. (Reporting by Rajendra Jadhav in Mumbai, Vu Khan in Hanoi, Chayut Setboonsarng in Bangkok, Ruma Paul in Bangladesh and Daksh Grover in Bengaluru; Editing by Vijay Kishore)