Top exporter India's 5% broken parboiled variety was quoted at $374-$378 a tonne this week, up slightly from $372-$375 a week ago.
"Rice production could fall in key states like West Bengal and Andhra Pradesh due to lower rainfall," said an exporter based at Kakinada in the southern state of Andhra Pradesh.
India received 14% less rainfall than the 50-year average in the week to Aug. 28, data from the India Meteorological Department (IMD) showed.
In neighbouring Bangladesh, Agriculture Minister Abdur Razzaque said the government is considering providing cash incentives to encourage rice exports.
Dhaka has been unable to clinch overseas deals since a long-standing export ban was lifted in May, with its rice more expensive than supplies from India or Thailand despite a recent fall in local prices.
Thailand's benchmark 5% broken rice prices were quoted at $410-$430 a tonne, a slightly narrower range from last week's $415-$430, traders said.
A firmer baht, Asia's best-performing currency this year, has kept prices high while supply shortages because of a continuing drought - the worst in a decade - has also played a major role in supporting prices.
The Thai government this week announced 21 billion baht ($682 million) of subsidies to help farmers affected by the drought and the strong baht.
Elsewhere, tepid demand kept rates for Vietnam's 5% broken rice unchanged from last week at $335-$340 a tonne amid slow trading activity.
"It's been quiet this week, with no major export deals, due to weak demand," said one trader based in Ho Chi Minh City.
Preliminary data showed only 29,600 tonnes of rice is scheduled to be loaded at Ho Chi Minh City ports over Sept. 1-10, with 23,000 tonnes bound for West Africa and the rest for the Philippines, traders said.
Government data released on Thursday showed Vietnam exported 4.53 million tonnes of rice in the first eight months of this year, little changed from the same period last year. August rice exports are estimated at 580,000 tonnes, compared with 598,619 tonnes in July.