The rupee has risen 6 percent so far in 2017 and is trading near its highest level in 21 months, trimming returns for exporters.
The strengthening rupee is also pushing up prices in dollar terms, making Indian supplies less competitive, said a rice exporter based in Kakinada in Andhra Pradesh.
Local paddy prices were firm on thinner supply.
"Paddy supply from winter crops is lower than anticipated," said another exporter based in Kakinada.
India mainly exports non-basmati rice to African countries and premier basmati rice to the Middle East.
Thai benchmark 5-percent broken rice remained at $360-$375 a tonne, free-on-board (FOB) Bangkok, in a quiet market.
"Prices will likely stay at this level for a while," a trader in Bangkok said.
The Thai government will open a state auction for 1.03 million tonnes of spoiled and sub-standard rice from state stockpiles on Friday.
Vietnams 5-percent broken rice dropped slightly to $350 a tonne, FOB Saigon, from $350-$355 last week, with traders citing a quiet market amid weak demand.
Rice exports by Vietnam in the first four months of 2017 are estimated to fall 7.7 percent from the same period last year to 1.86 million tonnes, the countrys farm ministry said on Wednesday.
Thailand and Vietnam are the worlds second and third biggest rice exporters.