NEW DELHI, May 10 (Reuters) - Indian Railways supply of trains to Coal India for transporting coal has fallen short of its monthly targets for more than a year, government data showed, highlighting the problems behind India's worst power crisis in over six years.

Indian utilities are scrambling to get hold of coal supplies to cope with record high power demand, but Indian Railways' inability to supply enough trains makes it difficult to boost coal stocks, which are at their lowest levels in years.

Inventories at Indian power plants fell 13% in April despite a 27.6% growth in Coal India's production, as a heatwave sent power demand soaring to a record high.

In April, state-run Indian Railways supplied 261 trains per day to Coal India for the power industry, the lowest in three months.

Indian Railways said at the end of April that it would cancel passenger trains to free up tracks and help to transport more coal to power plants.

Coal, which accounts for more than half of Indian Railways' freight revenue, makes up nearly 75% of India's power generation. State-run Coal India produces 80% of India's coal.

Indian Railways supply targets are set after deliberations between Indian Railways, the federal power ministry and Coal India.

Coal India has prioritized supply to utilities to avert a power crisis and its supplies to the non-power sector dropped to six month lows of 304,933 tonnes per day in April, 21.3% lower than the same period last year, based on government data.

Supplies to the non-power sector, which includes aluminum smelters and steel mills, were also hit by Indian Railways providing fewer trains. Coal India's supplies to the non-power sector via Indian Railways fell to its lowest level in six months, the data showed.

Officials from state-run aluminum producer NALCO filed a court case last month over a coal supply shortfall as a result of the diversion of coal supplies and a shortage of trains.

India's non-power sector have been taking more expensive power from the national grid due to a shortage in supplies of coal to their power plants, industry officials say.

(Reporting by Sudarshan Varadhan. Editing by Jane Merriman)