Aug 16 (Reuters) - Indian cotton prices are expected to rise marginally in the current week due to some export demand.

"Prices could go up marginally as traders are getting order from Bangladesh for cotton shipment," said an official, from Kolkata-based trading firm Wisdom Cotton.

Analysts and traders, however, expect lesser demand from domestic yarn makers which could cap the gains.

According to traders, there is very remote possibility for any sharp movement in prices as only two months are left for the new crop arrival.

India's cotton output is set for a second successive record harvest in 2011/12, up about 10 percent over last year's 32.5 million bales, a Reuters poll showed.

On Tuesday, the most traded Shankar-6 variety rose 1,000 rupees to 35,500 rupees per candy of 356 kg, showed data from trade body Cotton Association of India.

India, the world's second largest grower and exporter, allowed unrestricted exports for the remainder of the current season due to abundant availability of stocks.

India could export an additional 255,000 tonnes of cotton in these two months, traders said.

India's cotton output estimate for 2010/11 has been revised to 32.5 million bales from the earlier 31.2 million bales.

In June, responding to a demand from traders and farmers the government had allowed shipment of an extra 1 million cotton bales of 170 kg each, following a 30 percent decline in domestic prices since March.

It had already allowed shipment of 5.5 million bales in October last year.