Oct 21 (Reuters) - Cotton futures in India, the world's second-largest grower, are expected to fall this week on prospects of a bumper crop, arrivals from the new season harvest and weak demand from millers.

The Cotton Association of India (CAI), in its third crop estimate, has forecast a 7 percent rise in output to 38.1 million bales of 170 kg each in the year starting October 2013 due to increased yields.

"The available moisture (in soil) is likely to help increase yields and result in a larger-than-estimated crop. If the monsoon withdraws in the next few days, a better crop can be expected," Dhiren Sheth, president of CAI, said in a statement.

Supplies from the new harvest have started coming into the local markets in small quantities and are expected to gain pace in the coming weeks, spot traders said.

Daily arrivals have been around 65,000-75,000 bales and are expected to reach 90,000 bales by the next week, they said.

The government estimated cotton output in 2013/14 at a record high 35.3 million bales against 34 million bales a year earlier.

According to spot traders, cotton crop in Andhra Pradesh, the third-largest producer state, will not be affected much due to cyclone Phailin.

Most of the impact of the cyclone was limited to coastal regions, hence damage to cotton was limited in Andhra Pradesh, Kotak Commodities said in a research note.

Demand from millers remains weak in the absence of quality produce and subdued demand, traders said.

In September, India withdrew incentives for export of cotton and yarn, a value-added product used by textile mills, a move that could cut exporters' margins in the world's second-biggest exporter of the fibre.

The November cotton contract ended 0.15 percent lower at 20,160 rupees per bale of 170 kg each on the Multi Commodity Exchange on Monday.

In New York, the December cotton contract on the Intercontinental Exchange was up 0.19 percent at 83.27 cents per lb at 1229 GMT. (Reporting by Meenakshi Sharma; Editing by Prateek Chatterjee)